# 2017 AMC 12B Problems/Problem 16

## Problem 16

The number has over positive integer divisors. One of them is chosen at random. What is the probability that it is odd?

## Solution

If a factor of is odd, that means it contains no factors of . We can find the number of factors of two in by counting the number multiples of , , , and that are less than or equal to .After some quick counting we find that this number is . If the prime factorization of has factors of , there are choices for each divisor for how many factors of should be included ( to inclusive). The probability that a randomly chosen factor is odd is the same as if the number of factors of is which is .

Solution by: vedadehhc