Question

What is the greatest common factor of 27,36,72

Answer 1

The greatest common factor (GCF) of 27, 36, and 72 is: 9

To find the GCF we have to list the factors of each number we are given. In this case, 27, 36, and 72 is our numbers we have to list factors from. Our minimum factor is the original number we started with.

Factors of 27: 1, 3, 9, 27
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Find the common factor out of them, and then find the factor with the highest value. The common factors of each numbers are 1, 3, and 9. The highest number out of that is 9, so 9 is our GCF.

Answer 2

To find the greatest common factor, split each number up into prime factors using a method you like, the tree method is the method I was taught.

27 /3 = 9
9 /3 = 3
3 /3 = 1

27=3x3x3

36 /3 = 12
12 /3 = 4
4 /2 = 2
2 /2 = 1

36 = 3x3x2x2

72 /3 = 24
24 / 3 = 8
8 /2 = 4
4 /2 = 2
2 /2 = 1

72 = 3x3x2x2x2

Then, we must find the biggest number, and the fewest number of times it occurs. We can see that in 27 it appears 3 times, 36 twice, and 72 twice. Therefore the smallest number of times it appears is 2. 3x3=9, so the Greatest common factor of 27, 36, and 72 is 9.