Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 24"
(New page: ==Problem== {{empty}} ==Solution== {{solution}} ==See also== {{CYMO box|year=2006|l=Lyceum|num-b=23|num-a=25}}) |
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==Problem== | ==Problem== | ||
− | {{ | + | The number of divisors of the number <math>2006</math> is |
+ | |||
+ | <math>\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ 4\qquad\mathrm{(C)}\ 8\qquad\mathrm{(D)}\ 5\qquad\mathrm{(E)}\ 6</math> | ||
==Solution== | ==Solution== | ||
− | { | + | <math>2006=2\cdot17\cdot59</math>. A divisor of <math>2006</math> is therefore in the form <math>2^m\cdot 17^n\cdot 59^p</math>, where <math>m\leq 1</math>, <math>n\leq 1</math>, and <math>p\leq 1</math>. |
+ | |||
+ | There are 2 choices for <math>m</math>, 2 choices for <math>n</math>, and 2 choices for <math>p</math>. Therefore, there are <math>2\cdot2\cdot2=\boxed{8}</math> divisors of <math>2006</math>. | ||
==See also== | ==See also== | ||
{{CYMO box|year=2006|l=Lyceum|num-b=23|num-a=25}} | {{CYMO box|year=2006|l=Lyceum|num-b=23|num-a=25}} | ||
+ | |||
+ | [[Category:Introductory Algebra Problems]] |
Latest revision as of 12:15, 26 April 2008
Problem
The number of divisors of the number is
Solution
. A divisor of is therefore in the form , where , , and .
There are 2 choices for , 2 choices for , and 2 choices for . Therefore, there are divisors of .
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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