GMAT Math Questions | Number Properties

GMAT Sample Questions | Number of Factors

This GMAT Sample Math question is a Number Properties problem solving question and the concept covered is finding the number of factors or integral divisors of a number. A GMAT 650 to 700 level practice question.

Question 6: How many integral divisors does the number 120 have?

  1. 14
  2. 16
  3. 12
  4. 20
  5. None of these

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Explanatory Answer

Step 1 of solving this GMAT Number Properties Question: 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.

Step 2 of solving this GMAT Number Properties Question: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.

Key Takeaway
How to find the number of factors of a number? Method: Prime Factorization
Let the number be 'n'.
Step 1: Prime factorize 'n'. Let n = ap * bq, where 'a' and 'b' are the only prime factors of 'n'.
Step 2: Number of factors equals product of powers of primes incremented by 1.
i.e., number of factors = (p + 1)(q + 1)

 

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