Common Factors

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. 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.

Methods for Finding Common Factors

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.

Examples

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

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

Problem 1:

What are the Common factors of 8, 14, 18 and 22?

Answer:    

8   `->` 1, 2, 4, and 8

14 `->` 1, 2, 7 and 14

18 `->` 1, 2, 3, 6, 9 and 18

22 `->` 1, 2, 11 and 22

My forthcoming post is on Series Solutions of Differential Equations will give you more understanding about Algebra.

Problem 2:

What are the Common factors of 15, 30, 45 and 60?

Answer:    

15 `->` 1, 3, 5 and 15

30 `->` 1, 2, 3, 5, 6, 10, 15 and 30

45 `->` 1, 3, 5, 9, 15 and 45

60 `->` 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60