M4maths Previous Puzzles

21 Mar 2018 Perfect Squares

How many factors of 13699532025 are perfect squares?

OPtion

1) 12
2) 8
3) 16
4) 18
5) 25
6) 15
7) 30
8) 40
9) 24
10) None of these

Solution

13699532025 = 3^8 * 5^2 * 17^4

Any factor of this number should be of the form 3^a * 5^b * 17^c.

For the factor to be a perfect square a,b,c have to be even.

a can take values 0, 2, 4, 6, 8
b can take values 0, 2
and c can take values 0, 2, 4

Total number of perfect squares = 5 * 2 * 3 = 30

Correct Option: 7 Best Solution (0)