Common Factor of 2 Numbers

Introduction

To find the greatest common factor gcf of two given numbers,

• First we list all the factors of the two numbers.
• Then, we look for the common factors of these numbers.
• We find the greatest number among these common factors which will be the greatest common factor gcf of the two given numbers.

Problem 1:

Find the greatest common factor of 16 and 24.

Solution

Step 1:

The factors of 16 and 24 are

16 = 1, 2, 4, 8, 16

24 = 1, 2, 3, 4, 6, 8, 12, 24

Step 2:

The common factors of 16 and 24 are shown in bold.

Step 3:

The greatest among these is 8. So the greatest common factor gcf of 16 and 24 is 8.Problem 2:

Find the greatest common factor of 84 and 108.

Solution

Step 1:

The factors of 84 and 108 are

84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

Step 2:

The common factors of 84 and 108 are shown in bold.

Step 3:

The greatest among these is 12. So the greatest common factor gcf of 84 and 108 is 12.