Question

What is the greatest common factor of 32 and 48

Answer 1

The factors for 32 are −32,−16,−8,−4,−2,−1,1,2,4,8,16,32.

The factors for 48 are −48,−24,−16,−12,−8,−6,−4,−3,−2,−1,1,2,3,4,6,8,12,16,24,48.

List of all the factors for 32 and 48. 

32=−32,−16,−8,−4,−2,−1,1,2,4,8,16,32 
48=−48,−24,−16,−12,−8,−6,−4,−3,−2,−1,1,2,3,4,6,8,12,16,24,48

The common factors for 32,48 are −16,−8,−4,−2,−1,1,2,4,8,16.−16,−8,−4,−2,−1,1,2,4,8,16

The GCF of numerical factors −16,−8,−4,−2,−1,1,2,4,8,16 is 16.

16

Answer 2

Turn each number into the product of it's prime factors.

32=16x2=2x2x2x2x2=2^5

48=24*2=6x4x2=2x3x2x2x2

Pick the highest number that occurs. In this case it is 2. Now we have to see how many times it appears in both. It appears 5 times in 32 and 4 times in 48. 4 is the highest number of times it appears in the numbers so:

2^4=2x2x2x2=16

The Greatest Common Factor (GCF) of 32 and 48 is 16.