# Number Properties - Number of Divisors

Concept: Number of factors

The GMAT Sample Math question is a Number Systems question and the concept covered is finding the number of factors or integral divisors of a number.

#### Question: How many integral divisors does the number 120 have?

1. 14
2. 16
3. 12
4. 20
5. None of these

#### Video Explanation

##### Express the number in terms of its prime factors

120 = 23 * 3 * 5.
The three prime factors are 2, 3 and 5.
The powers of these prime factors are 3, 1 and 1 respectively.

##### Find the number of factors as follows

To find the number of factors / integral divisors that 120 has, increment the powers of each of the prime factors by 1 and then multiply them.

##### Number of factors = (3 + 1) * (1 + 1) * (1 + 1) = 4 * 2 * 2 = 16.

Choice B is the correct answer.

### Are you targeting Q-51 in GMAT Quant? Make it a reality!

Comprehensive Online classes for GMAT Math. 20 topics.
Focused preparation for the hard-to-crack eggs in the GMAT basket!