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?

1. 20
2. 4
3. 54
4. 32

Correct Answer - 54. Choice (3)

Explanatory Answer

Express 7200 as a product of prime numbers.
We get 7200 = 2⁵ * 3² * 5².

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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