I guess the answer should be 42.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 !
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?
