GCF of two Numbers Calculator

Greatest Common Factor is the largest number by which both numbers can be divided exactly. There are numerous methods to find the GCF of two numbers and they are explained below. For the sake of your convenience, we have taken examples detailing the procedure step by step so that you will be familiar with the concept in a much better way.

Major methods by which you can find the GCF of two numbers are

• Factoring
• Prime Factorization

Finding GCF of two Numbers using Factoring Method

In order to find the GCF of two numbers using Factoring Methos firstly list out all the factors of each number. Factors are the numbers that divide the number evenly i.e. leaving a remainder zero. In the Common Factor List of given numbers, GCF is the largest number common to each of the lists.

Example:

Find the GCF of numbers 18, 27?

Solution:

Given Inputs are 18, 27

Initially, find the factors of both the numbers 18, 27

Factors of 18 are 1, 2, 3, 6, 9, 18

Factors of 27 are 1, 3, 9, 27

Common Factors of 18, 27 are 1, 3, 9

In the factors of both the numbers, GCF is 9 as it is the largest number common to each of the lists.

Therefore, GCF of two numbers 18, 27 is 9

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Finding GCF of two numbers using Prime Factorization Method

To find the GCF of two numbers list all the prime factors of the given number. After that, find the prime factors that are common to each of the original numbers. Make a note of the highest number of occurrences of each prime number common to each original number. Multiply them together to get the Greatest Common Factor.

Example

Find the GCF of 15, 50 using Prime Factorization Method

Solution:

Given Input numbers are 15, 50

Firstly find the Prime factors of given input numbers i.e. 15, 50

Prime Factorization of 15 is 3x5

Prime Factorization of 50 is 2x5x5

Occurrences of Common Prime Factors is 5

Thus, GCF of 15, 50 is 5

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1. What is the full form of GCF?

GCF stands for Greatest Common Factor of Greatest Common Divisor.

2. What is meant by GCF?

Greatest Common Factor is the largest number by which both numbers can be divided exactly.

3. What are the methods to find GCF?

There are various methods to find GCF. The most efficient way usually depends on how many numbers you have and how large they are. Some of them are Factoring Method, Prime Factorization Method, Euclid's Algorithm.

4. How to find GCF easily?

Take the help of the GCF Calculator prevailing on this page to find the Greatest Common Factor easily. You just need to input the data and click on the enter button to avail the result GCF in no time.