2005 AMC 10A Problems/Problem 21
Contents
Problem
For how many positive integers does
evenly divide
?
Solution
By a standard result, , so this will evenly divide
precisely if
is an integer, or equivalently,
is a factor of
.
The positive factors of are
,
,
,
,
, and
(i.e.
factors in total), but as
must be a positive integer, we must have
. Therefore, the factor
cannot be used, but all the others can, giving
possible values of
(namely,
can be
,
,
,
, or
).
Video Solution
See also
2005 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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 | ||
All AMC 10 Problems and Solutions |
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