The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? Choices
A) 3	B) 14	C) 30	D) 42	E) 70
Let's try the Prime Box Approach   Prime Box is simply a collection of all prime factors of a given number!   (1) Prime Box of 16 = |2, 2, 2, 2|   (2) Prime Box of 45 = |3, 3, 5|   (3) Prime Box of n = |2, 2, 3....|   (4) Prime Box of 210 = |2, 5, 3, 7|   From 3 and 4:   The GCF of n and 210 must be a multiple of 6.   So we can eliminate A, B and E!   From 2 and 3:   n is not a multiple of 5. If it were, the GCF of n and 45 would have been 15!   So we can eliminate C   The only remaining choice is '42'
<result>D</result>
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?