Number Properties - Factors / Divisors

Concept: Prime factorization & divisibility

This GMAT practice question is a number theory question testing your understanding of factors/divisors of a number. You could get 2 to 4 questions testing concepts in number properties and number theory in the GMAT quant section.

Question: If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of 'a'?

  1. 121
  2. 3267
  3. 363
  4. 33
  5. None of the above

Video Explanation

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Explanatory Answer

Step 1: Prime factorize the given expression

a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311

Step 2: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33

112 is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should have been in 'a'

33 is a factor of the given number.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.

Therefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.

The smallest value that a can take is 363.

Choice C is the correct answer.

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