The GMAT Sample Math question for the day is from the topic Number Systems. The question is about finding the number of factors or integral divisors for a number.

Question
How many integral divisors does the number 120 have?

A. 14
B. 16
C. 12
D. 20
E. None of these

The correct choice is (B) and the correct answer is 16.

Explanatory Answer
Express the number 120 as a product of powers of prime factors.

In this case, 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.

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

In this case, (3+1) * (1 + 1) * (1 + 1) = 4 * 2 *2 = 16.

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