How many factors of 25 × 36 × 52 are perfect squares?

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This question belongs to Arithmetic Ability Permutation And Combination

Permutation and Combination

?

How many factors of 2⁵ × 3⁶ × 5² are perfect squares?

A) 20 B) 24 C) 30 D) 36

Answer & Solution

Correct Answer: Option B

Any factor of this number should be of the form 2^a × 3^b × 5^c
For the factor to be a perfect square a, b, c have to be even.
a can take values 0, 2, 4, b can take values 0, 2, 4, 6 and c can take values 0, 2
Total number of perfect squares =3 × 4 × 2 = 24

Question posted by Examveda

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