GCF of two Numbers Calculator

In Mathematics, Greatest Common Factor or Greatest Common Divisor of two numbers is the largest integer by which both the integers can be divided.

For instance, if you take the numbers 32, 256 the GCF of them would be 32 as it is the largest number that divides exactly both the given numbers.

GCF(32, 256) = 32

There are a number of ways in which you can find the Greatest Common Factor. However, which method would be appropriate will mostly depend on the numbers you are having, how large they are, and what you are going to do with the result.

There are three major methods by which you can find the GCF of numbers and they are as follows

• Factoring
• Prime Factorization
• Euclid’s Algorithm

Let’s get deep into each of the method by taking enough examples so that you will understand the concept of the Greatest Common Factor of two numbers easily.

In order to find GCF of two numbers using Factoring list out all factors of each number. Whole number factors are those that divide the number evenly leaving a remainder zero. Once you know the list of common factors GCF is the largest number common in each of the list.

Example

Find the GCF of numbers 36 and 45?

Solution:

Given numbers are 36 and 45

List of Positive Integers for the number 36 leaving a remainder zero is 1, 2, 3, 4, 6, 9, 18, 36

List of Positive Integers for the number 45 leaving a remainder zero is 1, 3, 5, 9, 15, 45

Greatest Common Factor of (36,45) that is largest and common in both the factors is 9.

Thus, GCF of 36, 45 is 9.

In order to find the GCF of numbers using the prime factorization method list the prime factors of each number. List the Prime numbers that are common to each of the numbers. Include the highest number of occurrences of each prime number common to each original number. Multiply them to get the Greatest Common Factor.

You will find prime factorization easier compared to the factoring method when the numbers are large.

Example

Find the GCF of numbers 15, 45 using the Prime Factorization Method?

Solution:

Prime factorization of 15 is 3 x 5

Prime factorization of 45 is 3 x 3 x 5

The highest number of occurrences of each prime number common to each original number is 3*5 and on multiplying you will get the GCF as 15

GCF of (15,45) is 15

If you want to find the GCF of two numbers using Prime Factorization and Factoring methods can be handy if the numbers are small. However, in the cases of large numbers factoring can be difficult. Euclid’s method of finding GCF can be a prime savior in such a case and eases your burden.

Steps to find GCF using Euclid’s Algorithm

• When given two numbers subtract the smaller number from the larger number and note the result.
• Continue the process subtracting the smaller number from the result until the result is smaller than the original smaller number.
• Use the original small number as a new large number and subtract the result you got in step from a new large number.
• Repeat the same process for every new large number and continue until you reach zero.
• Once you reach zero, go back to a step before and GCF is the number before the zero results.

Example

Find the GCF of (351,221) using Euclid’s Algorithm?

Solution:

In the given case numbers are 351, 221

Subtract the small number from the largest number i.e. 351 – 221 = 130

Subtract the result from the new large number i.e. 221 – 130 = 91

Repeat the same until you get zero i.e. 130 -91 = 39

Now it goes on further as such 91 – 39 = 52

and then 52 – 39 = 13

39 -13 = 26

26 -13 = 13

13 – 13 = 0

GCF is the number before the zero result and it is 13 in this case.

Thus, the GCF of (331, 221) is 13.

Take the help of lcmgcf.com designed GCF Calculator and save your valuable time in calculating the lengthy greatest common factor of two numbers problems.

1. How do you find the GCF?

You can find the GCF of numbers using any of the methods explained above. Depending on your comfort go with any of the three methods and find a solution.

2. Where can I get numerous examples for finding GCF of two numbers?

You can find the GCF of two numbers using various methods with examples from here.

3. Where do I find a GCF Calculator that calculates GCF of numbers?

You can find the GCF Calculator that calculates GCF of numbers from our page. Just give the inputs and you will find the Greatest Common Factor easily.