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

(The explanation of the formula was a little vague, so I just posted a good solution.)
(linking Divisor to the article.)
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==Problem==
 
==Problem==
−
The number of divisors of the number <math>2006</math> is
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The number of [[divisors]] of the number <math>2006</math> is
  
 
A. <math>3</math>
 
A. <math>3</math>

Revision as of 15:17, 2 March 2008

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 $2006$.

See also

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
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