Greatest Common Factor of 3 Numbers

Introduction

Given three numbers, the method of finding greatest common factor is same as the method of finding gcf of two numbers.

• We list all the factors of the three numbers.
• We look for the common factors of these numbers.
• Among these we find for the greatest number which will be the gcf of the three given numbers.

Problem 1:

Find the greatest common factor of 18, 24 and 36

Solution

Step 1:

The factors of 18 and 24 and 36 are

18 = 1, 2, 3, 6, 9, 18

24 = 1, 2, 3, 4, 6, 8, 12, 24

36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

Step 2:

The common factors of 18, 24 and 36 are shown in bold.

Step 3:

The greatest among these is 6. So the greatest common factor gcf of 18, 24 and 36 is 6.Problem 2:

Find the greatest common factor of 15, 35 and 75

Solution

Step 1:

The factors of 15, 35 and 75 are

15 = 1, 3, 5, 15

35 = 1, 5, 7, 35

75 = 1, 3, 5, 15, 25, 75

Step 2:

The common factors of 15, 35 and 75 are shown in bold.

Step 3:

The greatest among these is 5. So the greatest common factor gcf of 15, 35 and 75 is 5.