kman 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

Experts, please help how I should approach this...thx

good question :

My approach :

GCD between 16,n is 4 => n is a multiple of 5 => n=4*k

k cannot be even number needs to be odd and can be 5,7,9,etc

GCD of n and 45 is 3 => n=3*m =>

m cannot be multiple of 3 or 5 m can be any other odd numbers like 7,19 etc and any even number such as 2,4,6,etc

now combine both conditions => n=4*3*L where L can be odd numbers except multiple of 3,5

hence lets factorise 210

210=5*3*2*7 already n has 2,3 and we know 5 cannot occur in factors of n hence

largest possible GCD can be 3*2*7 =42

IMO D

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