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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