GCF of two or More Numbers Calculator

GCF of two or more Numbers Calculator: The Greatest Common Factor (GCF) Calculator is used to calculate GCF of two or more whole numbers. Here, you can enter numbers separated by a comma “,” and then press the Calculate button to get the GCF of those numbers.

Greatest Common Factor (GCF) Calculator is the most excellent handy calculator for calculating GCF!

Greatest Common Factor (GCF) Calculator f0r two or more Numbers

What is a Factor?

Factors are the numbers that we can multiply to each other to get one different number like 4 x 5 = 20, here 4 and 5 are factors

It is also possible to have various factors of a number like

4 x 5 = 20, 2 x 10 = 20, 1 x 20 = 20

Factors of 20: 1, 2, 4, 5, 10, and 20

What is a Common Factor?

So when we are finding the factors of two numbers like

Factors of 12 of 1, 2, 3, 4, 6, and 12

Factors of 20 of 1, 2, 4, 5, 10, and 20

So here common factors are 1, 2, and 4

A common factor is a factor of two or more numbers.

What is the Greatest Common Factor (GCF)?

Greatest Common Factor is just the biggest of the common factors. We can define it as:

The GCF is the greatest positive whole number from the set of a number that divides equally into all numbers with zero remainders.

So here if we are taking the previous example, then the Greatest Common Factor of 12 and 20 is 4.

Then, What is the Greatest Common Factor of 0?

We know that when we multiply any whole number to zero, it becomes zero so it is clear that each non zero whole number is a factor of 0. Like

n × 0 = 0 so, 0 ÷ n = 0, where n is any whole number

So GCF(n,0) = n, where n is any whole number

But, GCF(0, 0) is undefined.

How to Get the Greatest Common Factor (GCF) of Any Numbers?

There are so many ways available to find out the greatest common factor of any whole numbers such as Factoring, Prime Factorization, Euclid’s Algorithm, and many more. Which one of the methods is useful for you is decided by some factors like

  1. How many numbers are there?
  2. How long are the numbers?
  3. What is the purpose of finding the GCF?

So, go for any of the methods and get your GCF. Let’s go through each method in detail.

1.Factoring

Here, to check the Greatest Common Factor using the factoring method, we have to find out all the factors of each number manually or you can use any online Factors calculators also. So check out all the positive whole number factors of a number that can divide equally into the integers with zero remainders. Now write down all the common factors for each number, then find the biggest common number, it the GCF of numbers.

For detailed information see our Factoring Calculator.

Let’s check this with some examples to make it more simple,
Example 1:

Factors of 16: 1, 2, 4, 8, and 16

Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24

The common factor of 16 and 24: 1, 2, 4, and 8

The greatest common factor of 16 and 24: 8.

Example 2:

Factors of 15: 1, 3, 5, and 15

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30

Factors of 105: 1, 3, 5, 7, 15, 21, 35 and 105

Common factors of 15, 30 and 105: 1, 3, 5 and 15

Greatest Common Factor of 15, 30, and 105: 15.

2. Prime Factorization

Prime Factorization is helpful when numbers are larger. If you want to calculate the Greatest Common Factor using prime factorization, then you have to check out all of the prime factors of each number manually or you can check it with an online Prime Factors Calculator. Now from the prime factors, list out all the common prime factors of the numbers. Find out the maximum same numbers from each prime factor and multiply them to find out the Greatest Common Factor.

For detailed information see our Prime Factorisation Calculator.

Example 1: Find out GCF of 16 and 24?

Prime Factorization of 16 = 2 x 2 x 2 x 2

Prime Factorization of 24 = 2 x 2 x 2 x 3

The occurrence of common prime factor of 16 and 24: 2, 2 and 2

The greatest common factor of 16 and 24 is 2 x 2 x 2 = 8.

Example 2: Find out GCF of 15, 30 and 105

Prime factorization of 15 = 3 x 5

Prime factorization of 30 = 2 x 3 x 5

Prime factorization of 105 = 3 x 5 x 7

Common factors of 15, 30 and 105 = 3 and 5

Greatest Common Factor of 15, 30, and 105 = 3 x 5 = 15

3. Euclid’s Algorithm

Now, what if we are required to check the greatest common factor of very large numbers like 134334, 124456, or 187644? Some online calculators like Greatest Common Factor (GCF) or Factoring Calculator can help to find out the GCF of such a large number but what if you need to do it manually by yourself.

Step by step procedure to find the GCF of larger numbers with the help of Euclid’s Algorithm

  1. From the given numbers, first of all, take 2 whole numbers, and from the big number subtract the smaller number and write the result.
  2. Now subtract the small number from the result. Do it again and again till the result is less than the original small number.
  3. Now use the small number as a larger number and subtract the result you got from step two. Repeat the same procedure for every new bigger number and smaller number till you get the 0.
  4. Now if you get 0, then go back to one step before you get 0, the greatest common factor is the number you got just before the 0.

For detailed information see our Euclid’s Algorithm Calculator.

Let’s check it out with some examples.

Example 1: Find out GCF of 16 and 24

24 – 16 = 8

16 – 8 – 8 = 0

So, the GCF of 16 and 24 is 8, the least result we had before we got zero.

Example 2: Find out GCF of 15, 25 and 105

Here we have 3 numbers and for this, the method of finding GCF is:

GCF (x,y,z) = GCF (GCF (x,y),z)

So here we have to, first of all, find the greatest finding factor of 2 numbers and then we use its result with the 3rd number and find the GCF.

So Let’s get GCF (105, 25) first here,

105 – 25 = 80

80 – 25 = 55

55 – 25 = 30

30 – 25 = 5

25 – 5 = 20

20 – 5 – 5 – 5- 5 = 0

So, the greatest common factor of 105 and 25 is 5.

Now let’s check GCF of 3rd number, 15, and our result is also 5, GCF (5, 15)

15 – 5 – 5 – 5 = 0

So, the GCF of 15 and 5 is 5.

Therefore, the greatest common factor of 105, 25, and 15 is 5.

Example 3: Find the GCF 268442, 178296, and 66888

First of all, let’s find the GCF (268442, 178296)

268442 – 178296 = 90146

178296 – 90146 = 88150

90146 – 88150 = 1996

88150 – (1996 x 44) = 326

1996 – (326 x 6) = 40

326 – (40 x 8) = 6

40 – (6 x 6) = 4

6 – 4 = 2

4 – (2 x 2) =

So, the greatest common factor of 268442 and 178296 is 2.

Now we check the GCF (2, 66888)

66888 – (2 x 33444) = 0

So, the GCF of 2 and 66888: 2.

Hence, the GCF of 1268442, 178296, and 66888 is 2

Prime Factorization Calculator

Prime Factorization Calculator used to calculate the prime factorization of the number you enter here. (Numbers above 10 million may or may not time out. When you have to find out the Prime Factorization of very large numbers, the Prime Factorization Calculator can be very handy and useful.

The prime factorization calculator can help you to find prime factors of any integer number up to 1 trillion. Just enter the number here in the calculator and within no time you’ll get the prime factorization.

Prime Factorization Calculator various applications:

  • Check Prime factors of an integer number up to 1 trillion
  • Also, it can check either a number is prime or not
  • Prime decomposition in an exponential way
  • Make a list of all positive prime numbers smaller than the number you entered and calculate them
  • Comma-separated Values (CSV) of prime factors

To know the complete process, first of all, you must know all about what is a prime number?

A prime number is a positive whole number that is greater than 1 and that can be divided equally just by one and by itself. We can also say that cannot be achieved by multiplying 2 smaller numbers than that. Like 7 is a prime number! You can divide it by 1 or 7 only.

if an integer number is small then it’s very simple to decide whether a number is prime or not. For small numbers, we can use the rules of divisibility and trial division manually. But what if a number is very large and we have to determine whether it is prime or not. It is hard to check it manually as factoring large numbers carry very large primes. In such situations, an online calculator is the best to choose.

What is the prime factor?

Factors of prime numbers are prime factors. So here if we consider the factors of 12, that is, we need to get what integer numbers multiply to provide you 12. We understand that 1 * 12 = 12, 2 * 6 = 12 and 3 * 4 = 12. But here 12, 6, and 4 are not prime factors. The only prime factors of 12 are 2 and 3. You can also check prime factors using a factor calculator.

What is Prime Factorization?

Any whole number can be uniquely described as the list of prime numbers and such representation is named the prime factorization, or canonical representation or integer factorization or prime decomposition. There is exactly one prime factorization for any positive integer number, and such positive integer has just 1 prime factorization.

How to Find Prime Factorization of a Number?

There are various processes to find out the Prime Factorization of a Number and you can choose any of one as per the need. Here, we try to include two of the methods of prime factorization:

  1. Trial division and
  2. Using prime factors trees.

Trial Division

One of the methods to check the Prime Factor of a number is trial division. Trial division consists of very easy and basic algorithms, though it is an extremely slow process. In this method, we have to check each number by dividing the composite number in question by the integer and deciding if, and how many times, the number can divide the number equally.

To make it more understandable, let go through an example:

To get the prime factorization of 48, we have to start with dividing it by the smallest prime 2

48 ÷ 2 = 24

24 ÷ 2 = 12

12 ÷ 2 = 6

6 ÷ 2 = 3

But, we can’t divide 3 by 2, but we can divide 3 by itself only

3 ÷ 3 = 1

So here he prime factorization of 48 = 2 X 2 X 2 X 2 X 3 = 2X 3

We can check it in a prime factorization calculator also. The algorithm used in the calculator and trial division may differ but the result is always the same.

Prime Decomposition

Another popular method to find prime factorization is known as prime decomposition and it includes the use of a factor tree. The factor tree diagram is an easy process to divide a number into its prime factors. To create a factor tree we have to break down the composite number into factors of the composite number till the numbers are prime.

There might be various methods to show the factor tree for any provided prime factorization.

Here let’s take an example of 48 to check the prime factor using prime decomposition method.

It doesn’t matter whether you are using a calculator or find yourself, the factorization will be unique always. And when there are very big numbers, the calculator is much more amazing!

FAQs on Prime Factorization

Question 1: What is Prime Factorization?

Answer 1: Prime factorization means getting all the prime numbers that are factors of a number.

Question 2: What is The Sieve of Eratosthenes?

Answer 2: Eratosthenes invented a sieve to find prime numbers. It generally removes composite numbers and keeps prime numbers.

Question 3: What is a Composite Number?

Answer 3: When an integer number has more than two factors it is known as a composite number.

Question 4: Why find Prime Factors?

Answer 4: Prime Numbers can not be broken down so they are the basic blocks of all numbers. and this can be very helpful when working with large numbers, like in Cryptography.

 

NCERT Solutions for Class 10 Hindi Kshitij क्षितिज भाग 2 | Chapterwise Class 10 Hindi Kshitij Updated for 2023-24

Chapter Wise NCERT Solutions for Class 10 Hindi Kshitij क्षितिज भाग 2

NCERT Solutions for Class 10 Hindi Kshitij (क्षितिज) भाग 2

NCERT Solutions for Class 10 Hindi Kshitij क्षितिज भाग 2

काव्य – खंड

गद्य – खंड

SCERT Kerala Textbooks for Class 10 Malayalam | Kerala State Syllabus 10th Standard Textbooks English Malayalam Medium

SCERT Kerala Textbooks for Class 10 Malayalam

SCERT Kerala Books Class 10 Malayalam: The State Council of Education Research and Training(SCERT Kerala) publishes Malayalam textbooks for Class 10. The SCERT Samagra Kerala Class 10th Malayalam textbooks are well known for it’s updated and thoroughly revised syllabus. The SCERT Kerala Malayalam Books are based on the latest exam pattern and Kerala State syllabus.

SCERT Kerala keeps on updating the Malayalam books with the help of the latest question papers of each year. The Class 10 Malayalam books of SCERT Kerala are very well known for its presentation. The use of SCERT Kerala State Books for Class 10 Malayalam is not only suitable for studying the regular syllabus of various boards but it can also be useful for the candidates appearing for various competitive exams, Engineering Entrance Exams, and Olympiads.

SCERT Kerala Class 10 Malayalam Books PDF Download

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We hope that this detailed article on SCERT Kerala Samagra Textbooks for Class 10 Malayalam helps you in your preparation and you crack the SSLC exams or competitive exams with excellent scores.

Free PDF Download of NCERT Science Solutions for Class 8 All Chapters

NCERT Solutions for class 8 Science PDF Download

NCERT is completely responsible for designing and publishing school books for CBSE students for all classes. Here we have curated the list of chapter-wise NCERT Solutions for Class 8 Science PDF as per the latest and updated 2021-22 CBSE Syllabus and Exam Pattern.

Kids who find learning the physics and biology concepts difficult at class 8 can go through this NCERT 8th Class Science Textbook Solutions PDF. Also, it provides extra guidance to students while preparation so gain proper knowledge about the subject and score well in the exams.

Chapter Wise CBSE NCERT Solutions for Class 8 Science Free PDF Download

All the solutions are prepared according to the latest syllabus prescribed by CBSE and strictly follow CCE marking scheme. So, you can trust this handy NCERT Solutions 8th Class Science Book and start your preparation for the exams.

The guidance that can provide after subject teacher classes is surely NCERT Solutions Class 8 Science book. Hence, download the free pdf NCERT class 8 science solutions for all chapters by clicking the link available here and experience a new approach to learn the subject.

MCQ Questions for Class 8 Science with Answers

Kids who want to prepare effectively for their term 1 board exams should practice more and more with MCQs for class 8 science. By using these Chapterwise Class 8 Science MCQ Questions with Answers, you can examine your preparation standards and then you can concentrate on the weak areas before exams. Get a good grip on all the concepts of physics and biology with multiple choice questions and answers of 8th class and score well in the exams.

  1. Crop Production and Management Class 8 MCQ Questions
  2. Microorganisms: Friend and Foe Class 8 MCQ Questions
  3. Synthetic Fibres and Plastics Class 8 MCQ Questions
  4. Materials: Metals and Non-Metals Class 8 MCQ Questions
  5. Coal and Petroleum Class 8 MCQ Questions
  6. Combustion and Flame Class 8 MCQ Questions
  7. Conservation of Plants and Animals Class 8 MCQ Questions
  8. Cell Structure and Functions Class 8 MCQ Questions
  9. Reproduction in Animals Class 8 MCQ Questions
  10. Reaching the Age of Adolescence Class 8 MCQ
  11. Force and Pressure Class 8 MCQ
  12. Friction Class 8 MCQ
  13. Sound Class 8 MCQ Questions
  14. Chemical Effects of Electric Current Class 8 MCQ Questions
  15. Some Natural Phenomena Class 8 MCQ Questions
  16. Light Class 8 MCQ Questions
  17. Stars and the Solar System Class 8 MCQ Questions
  18. Pollution of Air and Water Class 8 MCQ Questions

NCERT Solutions for class 8 Science PDF Download

NCERT Class 8 Science Solutions Chapter Brief

Science and Maths are two important subjects that can make you face any kind of situation in a real-life. Also, with a great grip on fundamental concepts of science, it can be very easy to understand the advanced concepts in higher studies. In the updated CBSE Syllabus of Class 8 Science, there are 18 chapters present in the NCERT science textbook. All the solutions are given chapter-wise with proper elaborations and techniques to solve them.

CBSE NCERT Solutions for Class 8 Science Chapter 1 Crop Production and Management

Chapter 1 Crop Production covers all important concepts that help students to understand fertilizing, agriculture, etc. Simply go with the quick links available above and learn what are the types of Agricultural Practices, Basic Practices of Crop Production, Irrigation, Preparation of Soil, Sowing, Harvesting and Storage of Crops, Adding Manure and Fertilisers, Protection from Weeds.

CBSE NCERT Solutions for Class 8 Science Chapter 2 Microorganisms: Friend and Foe

In this chapter, students will get to learn how microbes play a vital role in our lives with different examples. Moreover, it explains the definition of microorganisms and then its major concepts like food preservation, places where microorganisms live, microorganisms and us, nitrogen fixation harmful microorganisms, and nitrogen cycle.

The following are the types of microorganisms involved in NCERT class 8 science solutions chapter 2:

  • Bacteria
  • Fungi
  • Protozoa
  • Algae
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NCERT Solutions for Class 8 Science Chapter 3 Synthetic Fibres and Plastics

This Chapter describes the synthetic fibres and its’ type (rayon, nylon, polyester, and acrylic). Along with such concepts, you will also find some more important concepts like Classification of synthetic fibers, characteristics of synthetic fibers, plastics, plastic as materials of choice, etc. Moreover, Class 8 Students will be familiar with the good qualities of plastic that are light in weight, strong and durable, cheap in cost, and a poor conductor of heat and electricity.

CBSE NCERT Solutions for Class 8 Science Chapter 4 Materials: Metals and Non-Metals

NCERT Solutions Class 8 Science Chapter 4 deals with the metals and non-metals concepts solutions for all the questions covered in the NCERT Textbooks. By learning this chapter, students will definitely learn the classification of components into metals and non-metals based on their properties. Along with this, you can also understand the concepts of Chemical Properties of Metals and Non-Metals, Uses of Metals and Non-Metals.

CBSE NCERT Solutions for Class 8 Science Chapter 5 Coal and Petroleum

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NCERT Solutions for Class 8 Science Chapter 6 Combustion and Flame

In the 6th chapter of Combustion and Flame, the major concepts that are explained are the chemical process of burning and the different types of flames. Moreover, there is a possibility to understand the negative points of combustion. Also, you will learn about various sorts of fuels are utilized for a different purpose at home, in industry and for running autos.

CBSE NCERT Solutions for Class 8 Science Chapter 7 Conservation of Plants and Animals

NCERT CBSE Class 8 Science Solutions for Chapter 7 aid students to study all about conserving plants and animals. The Conservation of Plants and Animals chapter completely provides detailed information about the topics like Biodiversity, Biosphere reserve, Deforestation, Desertification, Ecosystem, etc.

CBSE NCERT Solutions for Class 8 Science Chapter 8 Cell Structure and Functions

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NCERT Solutions for Class 8 Science Chapter 9 Reproduction in Animals

The concepts that are described in chapter 9 Reproduction in Animals will make you learn thoroughly about sexual reproduction where students will get familiar with the male reproductive organs, female reproductive organs, fertilization, development of the embryo, viviparous and oviparous animals. In short, it explains the modes and methods of reproduction in creatures.

CBSE NCERT Solutions for Class 8 Science Chapter 10 Reaching the Age of Adolescence

Class 8 Chapter 10 basically starts with the explanation of Adolescence and Puberty and the study of the human conceptive organs and the role of hormones in the development of an individual. Furthermore, it deals with the explanation of the topics of secondary sexual characters, sex determination, the role of hormones in initiating reproductive function, the role of hormones in completing the life history of insects and frogs, reproductive phase of life in humans, other hormones except for sex hormones, reproductive health.

CBSE NCERT Solutions for Class 8 Science Chapter 11 Force and Pressure

In this lesson ‘Force and Pressure’ NCERT 8th Science Solutions, students will come to know about the topics such as Force and types of force like contact force, electrostatic force, magnetic force, and many more.

NCERT Solutions for Class 8 Science Chapter 12 Friction

The chapter Friction deals with the concepts like Force of Friction, Factors affecting Friction, Friction: A Necessary Evil, Increasing and Reducing Friction, Wheels Reduce Friction, Fluid Friction.

CBSE NCERT Solutions for Class 8 Science Chapter 13 Sound

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CBSE NCERT Solutions for Class 8 Science Chapter 14 Chemical Effects of Electric Current

Here, it elaborates the concepts of “chemical effects of electric current” and electroplating. Basically, the chapter includes How Liquids Conduct Electricity, Chemical Effects of Electric Current, Electroplating Definition, and Process.

NCERT Solutions for Class 8 Science Chapter 15 Some Natural Phenomena

In this chapter, kids will come to discover the concepts such as lightning, Types of Charges and Their Interaction, Charging by Rubbing, Transfer of Charge, The Story of Lightning, Lightning Safety, and Earthquakes.

CBSE NCERT Solutions for Class 8 Science Chapter 16 Light

The chapter of Light covered in NCERT Solutions class 8 science deals with the key properties, impacts, and utilization of light and its subordinates. Moreover, this chapter will let us know the details about regular reflection, diffused reflection, laws of reflection, etc.

CBSE NCERT Solutions for Class 8 Science Chapter 17 Stars and the Solar System

In the Stars and the Solar System chapter, students will fully learn the concepts like Space, planets, comets, constellations, and the solar system. Basically, you will find the answers to the questions covered in chapter 17 of NCERT solutions for class 8 science.

NCERT Solutions for Class 8 Science Chapter 18 Pollution of Air and Water

The Pollution of Air and water chapter completely talks about the harmful changes that are taking place in our surroundings due to air and water pollution and its effect on human lives. It starts with some of the significant topics like Air pollution, how does air get polluted, further, the concept of the greenhouse effect and methods to reduce air pollution are explained in a simple language for easy understanding to students.

CBSE Class 8 Science Chapterwise NCERT Solutions will aid students as an authentic homework guide and the foundation for the annual board exam and competitive exam preparation like NEET and JEE. Designed NCERT 8th Class Solutions for Science chapters are error-free and easily lucid. Moreover, it helps kids to enhance basic concepts of the subject.

FAQs on CBSE Class 8 Science NCERT Solutions Chapter 1 to 18 PDF Download

1. How many chapters are explained in the Textbook Solutions of NCERT Science Class 8 PDF?

There are 18 chapters present in the NCERT Solutions for class 8 science is explained in a detailed way to help students understand the subject concepts.

2. Why NCERT Class 8 Science Solutions are important?

NCERT Solutions study resource is the best guide to learn and revise the complete syllabus of the class 8 science. However, NCERT Class 8 Science Solutions PDF helps students understand the concepts easily and solve all their doubts about the subject.

3. What are the benefits of utilizing NCERT Solutions for Class 8 Science?

The benefits of NCERT Solutions for Class 8 Science are as follows:

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  • As per the updated 2021-22 CBSE syllabus and exam pattern only subject experts framed these chapterwise NCERT Solutions for class 8 science.
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MCQs on Hybridisation

MCQs on Hybridisation for NEET

NEET  Chemistry is the scoring paper in the medical entrance examination. Here, you will discover the NEET Chemistry MCQ Questions for all Concepts as per the latest syllabus. Practice more on a regular basis with these NEET Chemistry objective questions on air pollution and improve your subject knowledge & problem-solving skills along with time management. NEET Chemistry Hybridisation Multiple Choice Questions make you feel confident in answering the question in the exam & increases your scores to high.

MCQs on Hybridisation

1. The compound which contains both ionic and covalent bond:
(a) KCl
(b) KCN
(c) CH4
(d) H2

Answer

Answer: (b)


2. The maximum number of 90o angles between bond pair-bond pair of electrons is observed in
(a) dsp2 hybridisation
(b) sp3d hybridisation
(c) dsp3 hybridisation
(d) sp3d2 hybridisation

Answer

Answer: (d)


3. Ether is more volatile than alcohol having the same molecular formula. This is due to
(a) alcohols having resonance structures
(b) intermolecular hydrogen bonding in ethers
(c) intermolecular hydrogen bonding in alcohols
(d) the dipolar character of ethers

Answer

Answer: (c)


4. The main axis of a diatomic molecule is z, molecular orbital px and py overlap to form which of the following orbital?
(a) pi molecular orbital
(b) sigma molecular orbital
(c) gamma molecular orbital
(d) No bond will be formed

Answer

Answer: (a)


5. Total number of lone pair of electrons in I3- ion is
(a) 3
(b) 6
(c) 9
(d) 12

Answer

Answer: (c)


6. BCl3 is a planar molecule whereas NCl3 is pyramidal because
(a) B-Cl bond is more polar than NaCl bond
(b) N-Cl bond is more covalent than B-Cl bond
(c) the nitrogen atom is smaller than boron atom
(d) BClhas no pair but NCl3 has a lone pair of electrons

Answer

Answer: (d)


7. In which solvent NaCl has maximum solubility?
(a) H2O
(b) C2H5OH
(c) CH3COCH3
(d) C2H5OC2H5

Answer

Answer: (a)


8. Which one of the following pairs of molecules will have permanent dipole moments for both members?
(a) NO2 and CO2
(b) NO2 and O3
(c) SiF4 and CO2
(d) SiF4 and NO2

Answer

Answer: (b)


9. Which of the following compounds has the smallest bond angle in its molecule?
(a) H2O
(b) H2S
(c) NH3
(d) SO2

Answer

Answer: (b)


10. Which one of the following properties is not shown by NO?
(a) it is diamagnetic in the gaseous state
(b) it is a neutral oxide
(c) it combines with oxygen to form nitrogen dioxide
(d) its bond order is 2.5

Answer

Answer: (a)