How many factors of 82044596000 are perfect squares?

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20 Sep 2017 Perfect Squares

How many factors of 82044596000 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

82044596000 = 2^5 * 5^3 * 29^5

Any factor of this number should be of the form 2^a * 5^b * 129^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
and c can take values 0, 2, 4

Total number of perfect squares = 3 * 2 * 3 = 18

Correct Option: 4 Best Solution (0)