If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72? Answers:
A) 24
B) 36
C) 12
D) 18
E) 16
The greatest common divisor of n and 16 is 4 --&gt; n is a multiple of 4 but not a multiple of 8.   The greatest common divisor of n and 15 is 3 --&gt; n is a multiple of 3 but not a multiple of 5.   72=2*3*3*2*2 is divisible by 12. therefore the greatest common divisor is 12   12
<result>C</result>
If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72?