How many factors are 2^5 3^6 5^2 are perfect squares: - Vidyadip

MCQ

How many factors are $2^5\times 3^6 \times 5^2$ are perfect squares:

✓
$24$
B
$12$
C
$16$
D
$22$

✓

Answer

Correct option: A.

$24$

Any factors of $2^5\times 3^6 \times 5^2$ which is a perfect square will be of the form $2^a \times 3^b \times 5^c$
where a can be $0$ or $2$ or $4,$
So there are $3$ ways.
$b$ can be $0$ or $2$ or $4$ or $6,$
So there are $4$ ways.
$a$ can be $0$ or $2,$
So there are $2$ ways.
So, the required number of factors $= 3 \times 4 \times 2 = 24$

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