# CAT Practice : Number System: Factors

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Beauty of the number 1001. This number is not prime, is a product of three distinct primes and does wonderful things to three-digit numbers when multiplied to them.

## 12 Factors

Q.13: What is the smallest number that has exactly 12 factors ?
1. 211
2. 60
3. 120
4. 144

Choice B. 60

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## Detailed Solution

A number of the form P1aP2bP3c will have (a + 1)(b + 1)(c + 1) factors where P1, P2, P3 are prime.

If a number has exactly 12 factors then (a + 1)(b + 1)(c + 1) should be equal to 12.

If the number has only one prime factor, it should be of the form.

P11 smallest no. possible = 211

If it has 2 prime factors, it can P13P22 or P15P2

23 x 32 or 25 x 3

72 or 96

If it has 3 prime factors it can be of the form

P1aP2bP3c

P1P2P3 = 22 x 3 x 5

P1P2P3 = 60

The smallest number possible = 60

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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.