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

A)6

B)12

C)24

D)36

E)48

The correct answer is B

n^2>=72*2=144=12^2

因为题目问 must divide n 所以当N取任何满足上面式子的数都必须成立！

在这个前提下，再问largest positive integer那就只能是12了。因为N也会等于144

清楚了吗？

quoted from Jennifer_ lam

题目解释的意思是能被72整除的能开平方的最小数是144，N就是12， 那么12/X, 能整除12的X的最大值(the samllest positiveinteger)是12。这题就是用整除概念来搞糊涂你。

If the question was like this,the answer would make sense. Thanks

If n is a positive integer and n^2 is divisible by 72,

=> n^2/72= n^2/ 6^2 *2, therefore n must at least be 12^2 in order to be divisible by 72.

then (the small positive) integer that must divide n is 12.