How many factors of 25 × 36 × 52 are perfect squares?
a) 20
b) 24
c) 30
d) 36
Answer: b
Explanation: Any factor of this number should be of the form 2a × 3b × 5c
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
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