What is the GCF of 16 and 72?

A.
16

B.
2

C.
8

D.
4

Question

What is the GCF of 16 and 72? 	
	
 
A.
	16
	
 
B.
	2
	
 
C.
	8
	
 
D.
	4

whpalmer4 · Answer

Well, as you get the luxury of choosing from 1 of 4 possible answers, you could just try them, starting from the largest, and selecting the largest one that divides evenly (read: is a factor of) into both 16 and 72.

whpalmer4 · Answer

To actually compute the answer:

Factor both numbers into their prime factorizations:

16=2*2*2*2 = 2^4
72=2*2*2*3*3 = 2^3*3^2

Now go through and collect the highest common power of all of the common factors, and multiply them together.  That's your GCF.

An example: find the GCF of 54 and 72

54 = 2*3*3*3 = 2^1*3^3
72 = 2*2*2*3*3 = 2^3*3^2

Highest common power of 2 is 2^1.  Highest common power of 3 is 3^2.  GCF is 2^1*3^2 = 2*9 = 18.