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 204? Choose one.
A) 34	B) 17	C) 48	D) 51	E) 102
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.   204=2*3*17*2 is divisible by 102. therefore the greatest common divisor is 102.   102
<result>E</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 204?