Question
How many factors of 25 * 36 * 52 are perfect squares?
CAT 2021
Solution
Correct option is
(B)
Explanatory Answer :
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