Question

How many factors of 1080 are perfect squares?

• A. $6$
• B. $8$
• C. $4$
• D. $5$

Answer 1

Answer: (C)

$4$

The factors of $1080$ which are perfect square:

$1080$ $\to$ $2^3$ $\times$ $3^3$ $\times$ $5$

For, a number to be perfect square, all the powers of number should be even number.

Power of $2$ $\to$ $0$ or $2$

Power of $3$ $\to$ $0$ or $2$

Power of $5$ $\to$ $0$

So, the factors which are perfect square are $1,4,9,36.$

Hence, Option C is correct.