OG 数学412

ghfgss231

If n is a positive integer and n的平方 is divisible by 72, then the largest positive integer that must divide n is

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

请教大家这个题的思路做法，谢谢大家。

bnbf

72 = 2^3 * 3^2
n^2 = 2^4 * 3^2
n = 2^2 * 3 = 12

recently

12 is the smallest one,
but if >12, we can't guarantee that it must divide n.
72=2*2*2*3*3.
72^1/2=3*2*(2^1/2)
but because n is a positive integer, so ,
the lease possible n is 3*2*2.