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

Explanatory Answer

Video explanation provided for this question
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.

Video Explanation

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