# Difficult Permutation-Combination Solved QuestionAptitude Discussion

 Q. How many factors of $2^4 × 5^3 × 7^4$ are odd numbers?
 ✔ A. $20$ ✖ B. $24$ ✖ C. $30$ ✖ D. $36$

Solution:
Option(A) is correct

Any factor of this number should be of the form $2^a × 3^b × 5^c$.

For the factor to be an odd number, $a$ should be $0$.

$b$ can take values $0,1, 2,3$ and $c$ can take values $0, 1, 2,3, 4.$

Total number of odd factors,

$= 4 × 5$

$= \textbf{20}$

## (1) Comment(s)

VEERARAGAVAN C S
()

there is a mistake in the first line.

it should be $2^a \times 5^b \times 7^c$. Since none of the factors of the given number is a multiple of 3