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

MCQ

How many factors are $ 2^5\times3^6\times5^2 $ are perfect squares:

✓
24
B
12
C
16
D
22

✓

Answer

Correct option: A.

24

Any factors of $ 2^5\times3^6\times5^2 $ which is a perfect square will be of the form $ 2^\text{a}\times3^\text{b}\times5^\text{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 $=3\times4\times2=24$

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