How many factors of 823851904000 are odd number?

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06 Feb 2019 Factors

How many factors of 823851904000 are odd number?

OPtion

1) 12
2) 8
3) 16
4) 18
5) 25
6) 15
7) 30
8) 36
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 odd number a should be 0

b can take values 0, 1, 2, 3
and c can take values 0, 1, 2, 3, 4, 5

Total number of odd factor = 4 * 6 = 24

Correct Option: 9 Best Solution (0)