Question

The number n has the form 3^x5^y where x and y are positive integers. You are given that 90/n is an integer. What is the greatest possible value of n?

A. 15
B. 30
C. 45
D. 90

Please SHOW me how to solve this, not just an answer. I am terrible with math.

Answer 1

Since 90/n is an integer, then the division of 90 by n should be an integer and the remaining should be 0
If n = 1 → 90/1 = 90
If n = 2 → 90/2 = 45
If n = 3 → 90/3 = 30
If n = 5 → 90/5 = 18
If n = 6 → 90/6 = 15
-------- -→ -------

if n = 90 → 90/90 = 1

So the maximum of n is 90 (answer D)