nik08 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

Can someone please explain this ?

Thanks !

I guess the answer should be 42.

16= 2*2*2*2
n=2*2

GCD = 4

45=3*3*5
n=3
GCD = 3

therefore n definitely consists of following

n=2*2*3 = 12

210 = 2*5*3*7

GCD = 2*3 = 6

In the answer options there are only 2 multiples of 6 i.e. 30 and 42

30 cannot be the GCD because n does not consists of 5 otherwise GCD of n and 45 should have one 5 as GCD.

42 can be GCD because n may consist of 7 as prime number.

Hence D.

Whats the OA?

D as well

yep the answer is 42 .

Thanks for the explainatn .. makes sense now

Thanks for the explanation.