Greatest Common Factor of 2 Numbers

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.

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.

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.