# CAT Practice : Number System: Factors

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How many factors does a number have? Thats a straightforward qn. How many factors of a number are odd; now thats an interesting variant.

## Number Theory - Odd Factors

Q.4: How many factors of 24 * 53 * 74 are odd numbers?
1. 100
2. 99
3. 20
4. 24

Choice C. 20.

## Detailed Solution

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

For the factor to be an odd number,
a should be 0.
b can take values 0, 1, 2, 3.
and c can take values 0, 1, 2, 3, 4.

Total number of odd factors = 4 * 5 = 20.
Choice (C)

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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.