How many factors of 1230356435 are perfect squares?

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10 May 2019 Perfect Squares

How many factors of 1230356435 are perfect squares?

OPtion

1) 12
2) 16
3) 9
4) 8
5) 6
6) 14
7) 20
8) 15
9) 24
10) None of these

Solution

1230356435 = 5^1 * 7^5 *11^4

Any factor of this number should be of the form 5^a * 7^b * 11^c.

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

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

Total number of perfect squares = 1 * 3 * 3 = 9

Correct Option: 3 Best Solution (0)