# CAT Practice : Number System: Factors

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We know how to find number of factors of a number. How do you find the number of factors that are perfect squares?

## Number Theory - Factors

Q.2: How many factors of 1080 are perfect squares?
1. 4
2. 6
3. 8
4. 5

Choice A. 4.

## Detailed Solution

1080 = 23 * 33 * 5. For any perfect square, all the powers of the primes have to be even numbers. So, if the factor is of the form 2a * 3b * 5c.

The values 'a' can take are 0 and 2, b can take are 0 and 2, and c can take the value 0.

Totally there are 4 possibilities. 1, 4, 9, and 36.

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## More questions from Number System - Factors

Dealing with factors of a number is a vital component in this topic. A range of questions can be asked based on this simple concept.