himu wrote: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?
3
14
30
42
70
210 = 2*3*5*7.
We need to determine which of these prime factors could be shared by n.
Since the GCF of n and 16 is 4, n is a multiple of 2.
Since the GCF of n and 45 is only 3, n a multiple of 3 but NOT of 5.
There is no condition that prevents n from being a multiple of 7.
Thus, of the prime factors of 210, n could share all but 5:
2*3*7 = 42.
The correct answer is
D.
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