Common Factors

Common Factors Definition, Examples | How to Find Common Factors?

A factor is a number that is the exact multiplicand of another number. Every number factor is less than or equal to the given number but it cannot be greater than the given number. Every number has at least 2 factors. Common factors are also the factors that are common to two or more numbers. Fet the detailed steps to find the common factors of 2 or more numbers, solved examples, and applications in the below sections.

What are Common Factors?

Common Factors are defined as the factors that are common to two or more numbers. You can also say that a common factor is a number with which a set of two or more numbers will be divided exactly.

To find the common factors of two numbers, you need to list the factors of each number separately and then compare them. Now write the factors which are common and those are called common factors for the given numbers.

How to find Common Factors?

Factors are the numbers that divide the original number. Here are the steps to check whether two or more numbers have common factors or not.

  • Get the factors of each number separately.
  • Compare the factors of two numbers.
  • If you find common numbers then those are common factors between two numbers.

Example:

Common Factors of 4, 12

Find the factors of given numbers

4 = 1, 2, 4

12 = 1, 2, 3, 4, 6, 12

The common factors between 4 and 12 are 1, 2, 4.

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Common Factors Examples

Example 1:

Find the common factors of 2, 16?

Solution:

The given numbers are 2, 16

Factors of 2 = 1, 2

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

Therefore, common factors of 2 and 16 = 1, 2.

Example 2:

Calculate the common factors of 14, 21?

Solution:

The given numbers are 14, 21

Factors of 14 = 1, 2, 7, 14

Factors of 21 = 1, 3, 7, 21

Therefore, common factors of 14 and 21 = 1, 7.

Example 3:

Find the common factors of 15, 45?

Solution:

The given numbers are 15, 45

Factors of 15 = 1, 3, 5, 15

Factors of 45 = 1, 3, 15, 5, 9, 45

Therefore, common factors of 15 and 45 = 1, 3, 5, 15.

Example 4:

Find the common factors of 36 and 63.

Solution:

The given numbers are 36, 63

The factors of 36 are

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

Stop here, since the number 6 is repeated.

So, 1, 2, 3, 4, 6, 9, 12, 18, and 36 are factors of 36.

The factors of 63 are

1 × 63 = 63

3 × 21 = 63

7 × 9 = 63

9 × 7 = 63

Stop here, since the numbers 7 and 9 are repeated.

So, 1, 3, 7, 9, 21, and 63 are factors of 63.

1, 3, and 9 are common in both lists.

Hence, the common factors of 36 and 63 are 1, 3, 9.

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