2003 AMC 12A Problems/Problem 8
Contents
Problem
What is the probability that a randomly drawn positive factor of is less than
Solution 1
For a positive number which is not a perfect square, exactly half of the positive factors will be less than
.
Since is not a perfect square, half of the positive factors of
will be less than
.
Clearly, there are no positive factors of between
and
.
Therefore half of the positive factors will be less than .
So the answer is .
Solution 2
Testing all numbers less than , numbers
, and
divide
. The prime factorization of
is
. Using the formula for the number of divisors, the total number of divisors of
is
. Therefore, our desired probability is