What is the gcf of 36 and 120 using a factor tree?

Answer 1

As drawing a factor tree is not easy here, I'll use brackets to represent the different branches:

36 = (6 × 6) = ((2 × 3) × (2 × 3) = [2] × [2] × [3] × 3

120 = (10 × 12) = ((2 × 5) × (3 × 4)) = ((2 × 5) × (3 × (2 × 2))) = [2] × [2] × 2 × [3] × 5

→ gcf(12, 54) = 2 × 2 × 3 = 12

Answer 2

72

36,2

18,2,2

9,2,2,2

3,3,2,2,2

120

60,2

30,2,2

15,2,2,2

5,3,2,2,2

2 x 2 x 2 x 3 = 24, the GCF

Answer 3

The factor tree will show you the prime factorization. You still need to compare that to another number to get a GCF.

Answer 4

2 x 2 x 2 x 3 x 5 = 120

3 x 3 x 3 x 3 x 5 = 405

3 x 5 = 15, the HCF

Prime factorization is easier.

Answer 5

12(10 + 3) = (12 x 10) + (12 x 3) = 12 x 13 = 156

Answer 6

The GCF is 4.

Answer 7

120 + 36 = 12*(10 + 3).

Answer 8

12

Answer 9

It is: 6