2006 Cyprus MO/Lyceum/Problem 24

Problem

The number of divisors of the number $2006$ is

A. $3$

B. $4$

C. $8$

D. $5$

E. $6$

Solution

$2006 = 2 \cdot 17 \cdot 59$ . 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 two choices for $p$ , therefore there are $2\cdot 2\cdot 2=\boxed{8}$ divisors of $2006$ .

2006 Cyprus MO, Lyceum (Problems)
Preceded by Problem 23	Followed by Problem 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

Page

Toolbox

Search

2006 Cyprus MO/Lyceum/Problem 24

Problem

Solution

See also