How many factors of 823851904000 are perfect squares?

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19 Jun 2020 Perfect Squares

How many factors of 823851904000 are perfect squares?

OPtion

1) 12
2) 8
3) 16
4) 36
5) 25
6) 15
7) 30
8) 18
9) 24
10) None of these

Solution

823851904000 = 2^10 * 5^3 *23^5

Any factor of this number should be of the form 2^a * 5^b * 23^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, 10
b can take values 0, 2
and c can take values 0, 2, 4

Total number of perfect squares = 6 * 2 * 3 = 36

Correct Option: 4 Best Solution (2)

Varun   3 years AGO

The factors are 2^10*5^3*23^5
The ones that forms square are 2^2,4^2,16^2,64^2,256^2,1024^2,5^2,23^2,23^4
=>9 *4
= 36
= Option (4)

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G.S.Kantharao   3 years AGO

No of perfect squares=36
My Option 4✍️

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