How many factors of 587042640 are perfect squares?

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12 Apr 2019 Perfect Square

How many factors of 587042640 are perfect squares?

OPtion

1) 24
2) 20
3) 12
4) 16
5) 18
6) 9
7) 27
8) 30
9) 20
10) None of these

Solution

587042640 = 73^2 * 17^1 * 5^1 * 3^4 * 2^4

Any factor of this number should be of the form 73^a * 17^b * 5^c * 3^d * 2^e

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

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


Total number of perfect squares = 2*1*1*3*3 = 18


Option 5)

Correct Option: 5 Best Solution (0)