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

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.

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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.

### 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.

### 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?

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.

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

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.

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.

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

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