What is the smallest positive integer n for which n∗7! is an integer?

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PS · Problem Solving

505-555

Number Properties

What is the smallest positive integer $n$ for which $\sqrt{n∗7!}$ is an integer?

Answer Choices

Correct answer marked below

A

14

35

Correct

C

70

D

105

E

210

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What this question tests

What it tests

Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.

Common trap

Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.

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What is the smallest positive integer nnn for which n∗7!\sqrt{n∗7!}n∗7!​ is an integer?