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

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Explanatory Answer

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.

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