We know that when N is written as a product of prime numbers, the power of 2 will be 2, since GCF(16,N)=4pkw209 wrote:The greatest common factor of 16 and the positive integer N is 4. The GCF of N and 45 is 3. Which of the following could be the GCF of N and 210?
a) 3
b) 14
c) 30
d) 42
e) 70
Answer is D
(N must be a multiple of 4, but not of 8, as the GCF is 4 )
Since GCF(N,45) is 3 and 45= 3^2 x 5, the power of 3 in the prime factorization of N is 3^1 and that of 5 is 5^0
Thus N = 2^2 x 3 x 5^0 x ...
210 = 2 x 3 x 5 x 7
Thus GCF(N, 210) = 2 X 3 x 7^x , where x is either 0 or 1
Therefore GCF(N, 210) is either 6 or 6 x 7= 42
