Problem Solving - 18

If n is a positive integer and n^2 is divisible by 72, then the largest possible positive integer that must divide n is

A) 6
B) 12
C) 24
D) 36
E) 48

Answer : B

Focus primarily on the word "must" and after that shift your focus to the word "largest"

n^2 = 72q = 36*2q = 6^2*2q , where 2q must be the square of a number
q = 2p^2 , where p is a +ve integer
Hence n = 12p

As such 12 is the largest possible number that must divide n.

Other numbers that must divide n would be 1,2,3,4,6.

Apart from these the possible numbers that may divide n could be any numbers, depending on what p is