# XAT Sample Question : Quant : Number Theory - Factors

The question is from the topic Number System and is about finding the number of factors of a positive integer.

## Question

How many divisors does 7200 have?

- 20
- 4
- 54
- 32

Correct Answer -

**54**. Choice (3)

#### Explanatory Answer

Express 7200 as a product of prime numbers.

We get 7200 = 2

^{5} * 3

^{2} * 5

^{2}.

If a number 'n' can be expressed as a

^{p} * b

^{q}, where a and b are prime factors of n, the number of factors of n = (p + 1)(q + 1)

Applying the above result, we get the number of different divisors of 7200 including 1 and 7200 = (5 + 1) (2 + 1) (2 + 1) = 6 * 3 * 3 = 54

Correct answer choice (3)

Level of difficulty : Moderate

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