# Problem of the Day

If a factor of the number is selected at random. What is the probability that it is odd?

A.

B.

C.

D.

E.

[latexpage]

B. $\frac{1}{4}$

See the Solution

### Solution

[latexpage]

$2^33^45^27^4$ has $4\cdot 5\cdot 3\cdot 5\cdot=300$ factors. If you don’t see why, look at the solution to the 8/26 Problem of the Day here:Â http://gmatmathpro.com/2011/08/26/problem-of-the-day-826/.

If a factor is odd, it must be composed entirely of odd prime factors. There are $5\cdot 3\cdot 5=75$ ways to choose only odd groups of prime factors from $2^33^45^27^4$, so the probability of any factor being odd is $\frac{75}{300}=\frac{1}{4}$