# Greatest Common Factor Calculator

Find the greatest common factor, common factors, and all factors for a set of numbers using our calculator.

The greatest common factor of a set of numbers is the largest factor that is common to all of the numbers.

A factor of a number x is a number that can be multiplied by another number to get x.

## Solution

$$The greatest common factor of 22, 88, & 132 is 22Find the factors for each numberThe factors of 22 are [1, 2, 11, 22]The factors of 88 are [1, 2, 4, 8, 11, 22, 44, 88]The factors of 132 are [1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132]Find the factors that are common to all 3 numbersCommon factors are [1, 2, 11, 22]The greatest common factor is the largest factor common to all 3 numbersGreatest common factor is 22$$

## How to Find the Greatest Common Factor of a Number

### Find the Greatest Common Factor Using Prime Factorization

To find the greatest common factor of 90 and 165 using prime factorization, find the prime factors of each number.

To find the prime factors, divide each number by another prime factor until they cannot be divided further.

To find the prime factors of 90, divide 90 by 2 to get 45. 2 is a prime number but 45 can be divided by 5 to get 9. 5 is a prime number but 9 can be divided by 3 to get 3. The prime numbers of 90 are [5,3,3,2].

Repeat this process for 165. 165 divided by 3 = 55. 3 is a prime factor but 55 can be divided by 5 to get 11. The prime factors of 165 are [11,5,3].

See our prime factors calculator to find all prime factors of a number.

Find the prime factors that are common to both numbers. 5 and 3 are common prime factors of 90 and 165. To find the greatest common factor, simply multiply the common prime factors together. 5 × 3 = 15, which is the greatest common factor of 90 and 165.

### Find the Greatest Common Factor By Finding All Factors

To find the greatest common factor of 90 and 165, start by finding the factors for both.

The factors for 90 are [1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90]

The factors for 165 are [1, 3, 5, 11, 15, 33, 55, 165]

The next step is to find the factors that are common to both 90 and 165.

The common factors are [1, 3, 5, 15]

The greatest common factor between 90 and 165 is 15.

## What is the Greatest Common Factor Used For

The greatest common factor is most commonly used to simplify or reduce fractions. The greatest common factor is also known as the greatest common divisor. Learn more about reducing fractions using our reducing fractions calculator.