How many factors of 2027229039 are perfect squares?

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09 Oct 2018 Perfect Square

How many factors of 2027229039 are perfect squares?

OPtion

1) 60
2) 18
3) 12
4) 9
5) 15
6) 16
7) 6
8) 24
9) 27
10) None of these

Solution

2027229039 = 23^3 * 17^1 * 11^2 * 3^4

Any factor of this number should be of the form 23^a * 17^b * 11^c * 3^d

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

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



Total number of perfect squares = 2*1*2*3 = 12

Option 3)

Correct Option: 3 Best Solution (0)