Common Factor with Examples and FAQs

What is a Common Factor?

Any number is a factor of a number if it divides the number without leaving any remainder behind. If two or more numbers share factors, i.e., a few of their factors are the same then the factors are termed as common factors.

For example,

The factors of 30 are 1, 2, 3, 5, 6, 10 and 15.

The factors of 35 are 1, 5, 7 and 35.

Here, ‘1’ and ‘5’ are the factors that are common for both 30 and 35. These factors are common factors.

Note: ‘1’ is a common factor of any two numbers. Even if two numbers share no factors in common they will always have ‘1’ as a common factor. These numbers are mutually prime or co-prime.

How to determine common factors of the given numbers?

The steps to determine the common factors are:

1. Determine all the factors of each of the given numbers.
2. Check which of the factors are common for the given numbers.

For example:

To determine the common factors of 45 and 60, at first, we write down the factors of 45 and 60.

Factors of  45 are 1, 3, 5, 9, 15 and 45.

Factors of 60 are  1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Hence the factors that are common for both are 1, 3, 5 and 15 which are the common factors of 45 and 60. 

Greatest Common Factor

After the common factors of a group of 2 or more numbers are determined the largest of those factors is known as the Greatest Common Factor (GCF). It is also known as the Highest Common Factor ( HCF).

For example, let us consider two numbers 56 and 84.

At first, we write down the factors of 56 and 84.

Factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.

Factors of 84 are  1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.

Hence the factors that are common for both are 1, 2, 4, 7, 14 and 28 which are the common factors of 56 and 84.

Now among the common factors, 28 is the greatest. Therefore, 28 is the GCF or 56 and 84.  

Examples

Example 1: What are the common factors of 24, 56 and 72?

Solution:

Identifying the factors of each number first,

Factors of 24 are 1, 2, 4, 6, 8, 12 and 24.

Factors of 56 are  1, 2, 4, 7, 8, 14, 28 and 56.

Factors of 72 are  1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

Hence, the common factors are 1, 2, 4, 8 and 12.

Example 2: What is the GCF of 48, 64 and 90?

Solution:

Identifying the factors of each number first,

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Factors of 64 are  1, 2, 4, 8, 16, 32 and 64.

Factors of 90 are  1, 2, 3, 5, 6,  9, 10, 15, 18, 30, 45 and 90.

The common factors are 1 and 2. Hence the GCF is 2.

Example 3: Determine the common factors of 45 and 58.

Solution:

Writing down the factors of each number first,

Factors of 45 are  1, 3, 5, 9, 15 and 45.

Factors of 58 are  1, 2, 29 and 58.

Hence the numbers 45 and 58 have just 1 as a common factor.

Note: 45 and 58 are coprime as they have only ‘1’ as their common factor.