Divisibility Question - Need a better explanation

[MoniqueK]

The question is #169 in the Quant Review book:

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 explanation provided in the book is not so clear to me. Can anyone help?

I find that I generally have trouble with such questions.

Here's another Data Sufficiency question that also pertains to divisibility (#110 in Quant Book)

Is the positive integer n a multiple of 24?

(1) n is a multiple of 4
(2) n is a multiple of 6.


When I review the concepts, I completely understand, yet I always have trouble with these sort of problems.

Thank you!

[iamcste]

The question is #169 in the Quant Review book:

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 explanation provided in the book is not so clear to me. Can anyone help?

I find that I generally have trouble with such questions.

Here's another Data Sufficiency question that also pertains to divisibility (#110 in Quant Book)

Is the positive integer n a multiple of 24?

(1) n is a multiple of 4
(2) n is a multiple of 6.


When I review the concepts, I completely understand, yet I always have trouble with these sort of problems.

Thank you!

Problem 1

https://www.beatthegmat.com/og-quant-rev ... 11652.html


Problem 2