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?

- 14
- 16
- 12
- 20
- None of these

#### Video Explanation

Scroll for explanatory answer text#### Explanatory Answer

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

120 = 2^{3} * 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.

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