mun23 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?

(A)3

(B)14

(C)30

(D)42

(E)70

Need easy explanation to solve it quickly

Hi, let me try to explain in simpler way:

GCF = 4 = 2^2

16 = 2^4

that means prime box of n = 2^2 , ? ? ?

GCF = 3

45 = 3^2*5

that means prime box of n = 3^1, ? ? ?

Overall prime box of n = 2^2, 3^1, ???

Now, 210 = 3*7*5*2

from above we know the prime factor and powers of n (not complete ??)

therefore GCF = 3^1 * 2^1 * 7^1 (not 5 - we have seen above, but at least a 7 is possible)

Thus at least a GCF of 42 is possible here

Hope this helps

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