Track / Stage 2 / 48 of 320 #368 of 2604

Problem 368

Number theory Difficulty 2.0 Find the answer UKMT Senior Mathematical Challenge · United Kingdom · 2015

What is the largest integer $k$ whose square $k^2$ is a factor of $10!$ ? $[10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1.]$ (A) $6$ (B) $256$ (C) $360$ (D) $720$ (E) $5040$

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.