If n is a positive integer and n^2 is divisible by 72, then the largest positive integer M that must divide n is?
Choose the correct option: A) 6 B) 12 C) 24 D) 36 E) 48

Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer m that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: B