vksunder wrote:

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

72 = (2^3)(3^2)We are told that

n^2 is divisible by

72. Because

n^2 is a perfect square, all its prime factors must have even exponents. Because 72 has a prime factor 2 with an odd exponent, which is 3, 72 lacks another 2 for the whole product to be at least a square of an integer. So if you multiply 72*2, you will get the perfect square 144. Therefore

sqrt(144) = 12, which is n. The largest positive integer that will divide n is itself, so it should be 12.

Answer B