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Common Factors


The two numbers has more than one similar factor that factors are called as common factor. The factors are used for common factor determination.

The common factors of two or more whole digits is the biggest whole digit that equally divides all the whole digits.

There are two methods to find common factors in math.

The initial method is to list all the factors of each digit and then decide the biggest factor.

For Example:

Find the common factors of 12 and 18.

The factors of 12 are 1, 2, 3, 4, 6 and 8.

The factors of 18 are 1, 2, 3, 6, 9 and 18.

The common factors of 12 and 18 are 1, 2 and 3.

Related Calculators
Calculate Greatest Common Factor Common Factor Calculator
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What is a Common Factor?

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The numbers are getting from multiplication of two numbers. That numbers are called as factors. For example, the factors of 6 are 1, 2, 3, 6. The same factors of two numbers are called as common factor. The number 1 is always common factor of all numbers.

How to Find Common Factor

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There are two methods to find the common factors of numbers. Listed below are the steps to be followed in finding common factors.

Method I:

  • List all the factors of the numbers.

  • Collect the common factors among each digit.

Method II:

  • Find the prime factors of each digit.

  • Merge the common terms of each digit.


Common Factor Examples

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Listed Below are some of the examples in finding the common factors.

Solved Examples

Question 1: What are the Common factors of 34 and 36?
Solution:
 
The factors of 34 are 1, 2, 17, and 34.

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

Now, using method 1,

The common factors to the two numbers are 1 and 2.

The Common factors of 34 and 36 are 1 and 2.
 

Question 2: What are the common factors of 40, 45 and 50?
Solution:
 
Prime factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

Prime factors of 45 are 1, 3, 5, 9, 15 and 45

Prime factors of 50 are 1, 2, 5, 10, 25, and 50.

Now, using method 2,

The common factors of 40, 45 and 50 are 1, 2 and 5.
 

Common Factors Practice Problems

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Listed below are some of the practice problems in finding the common factors.

Practice Problems

Question 1: What are the Common factors of 8, 14, 18 and 22?
Question 2: What are the Common factors of 15, 30, 45 and 60?
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