Question

# How many factors of 1080 are perfect squares?

CAT 2021

A
B
C
D
##### 5
Solution

Correct option is

(A)

There are four perfect square divisors:

1, 4, 9, and 36. ( It's easy to forget the 1. )

The prime factorization of 1080 = 2^3 • 3^3 • 5

In order for a divisor to be a perfect square, it must have an even number of 1s, 2s, 3s, or 5s. We have

$2^{2} = 4$

$3^{2} = 9$

$2^{2}*3^{2} = 4 * 9 = 36$

and $1^{2} = 1$

Perfect square divisors: 1, 4, 9, and 36

so , A is the correct option