Permutation-Combination
Aptitude

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Q.

How many factors of $2^4 × 5^3 × 7^4$ are odd numbers?

 A.

$20$

 B.

$24$

 C.

$30$

 D.

$36$

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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