How many factors of 2⁵ 3⁶ 5² are perfect squares?

Answer:- 1

Explanation:-

Solution:

Any factor of this number should be of the form 2^{a^*3b} *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.