# Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 24"

## Problem

The number of divisors of the number $2006$ is

$\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ 4\qquad\mathrm{(C)}\ 8\qquad\mathrm{(D)}\ 5\qquad\mathrm{(E)}\ 6$

## Solution

$2006=2\cdot17\cdot59$. A divisor of $2006$ is therefore in the form $2^m\cdot 17^n\cdot 59^p$, where $m\leq 1$, $n\leq 1$, and $p\leq 1$.

There are 2 choices for $m$, 2 choices for $n$, and 2 choices for $p$. Therefore, there are $2\cdot2\cdot2=\boxed{8}$ divisors of $2006$.

 2006 Cyprus MO, Lyceum (Problems) Preceded byProblem 23 Followed byProblem 25 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30