Question

Find the greatest common factor (GCF) for the following:

1. 4, 12, 16
2. 12, 18, 9
3. 22, 8, 28
4. 56, 16, 24

Answer 1

1. 4

2. 3.

3. 2

4. 8.

Explanation:

Find the GCF of 4, 12, 16 .

Write as prime factors:

4 = 2*2

12 = 2*2*3

16 = 2*2*2*2

Note that 2*2 is common to all 3 of three factors The GCF = 4.

Find the GCF of 12, 18 and 9, .

Write as prime factors:

12 = 2*2 * 3

18 = 2*3*3

9 = 3*3

Note that 3 is common to all 3 of the factors The GCF = 3.

Find the GCF of 22, 8 and 28:

Write as prime factors:

22 = 2*11

8 = 2*2*2

28 = 2*2*7

Note that 2 is common to all 3 of three factors The GCF = 2.

Find the GCF of 56, 16 and 24:

Write as prime factors:

16 = 2*2*2*2

24 = 2*2*2*3

56 = 2*2*2*7

Notice that 2*2*2 is common to all 3 factors , so the GCF = 8.