# CAT Practice : Number System: Factors

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Given a prime factorization, how do we find how many factors of the number are perfect squares.

## Number Theory - Factors

Q.3: How many factors of 25 * 36 * 52 are perfect squares?
1. 18
2. 24
3. 36
4. 8

Choice B. 24.

## Detailed Solution

Any factor of this number should be of the form 2a * 3b * 5c.

For the factor to be a perfect square a,b,c have to be even.

a can take values 0, 2, 4.
b can take values 0, 2, 4, 6
and c can take values 0, 2

Total number of perfect squares = 3 * 4 * 2 = 24. Choice (B).

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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.