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QUANTITATIVE REASONING · GMAT-Q-NP-01

Number Properties: Divisibility, Factors and Remainders

GMAT lesson development preview · DRAFT · Original learning and assessment material

Concepts and problem-solving strategy

Divisibility and prime factorization

Remainders and modular reasoning

Greatest common divisor and least common multiple

Think Like a GMAT Test-Taker

Determine whether the prompt asks for a factor, a multiple, a remainder, or a parity result. Translate words into a precise divisibility condition.

Faster Methods

For a remainder, write N = dq + r before testing cases.

Count positive divisors from prime exponents, not by writing every divisor.

Worked example 1

How many positive divisors does 72 have?

Each factor uses one of four exponents of 2 and one of three exponents of 3.

Worked example 2

What is the remainder when 173 is divided by 7?

The remainder is 5 because it lies between 0 and 6.

Common Traps

  • A remainder must be nonnegative and smaller than the divisor.
  • Do not confuse multiples with factors.
  • If a number is divisible by 6, it must be divisible by both 2 and 3.
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