ikaplan wrote:If k is a positive integer and the greatest common divisor of k and 45 is 15, then the greatest common divisor of k and 900 may be any of the following EXCEPT
(A) 15
(B) 45
(C) 60
(D) 150
(E) 300
Since the greatest integer that divides into both k and 45 is 15, k cannot be a multiple of 45.
To illustrate:
If k=90 -- a multiple of 45 -- then the GCF of k=90 and 45 would be 45, not 15.
Since k cannot be divisible by 45, the GCF of k and 900 cannot be divisible by 45.
Thus, the GCF of k and 900 cannot be answer choice
B.
The correct answer is
B.
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