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

Solution (By Examveda Team)

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