How many factors of 105488578125 are odd number?

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04 Sep 2019 Factors

How many factors of 105488578125 are odd number?

OPtion

1) 200
2) 48
3) 180
4) 300
5) 280
6) 160
7) 360
8) 320
9) 40
10) None of these

Solution

105488578125 = 3^9 * 5^6 * 7^3

Any factor of this number should be of the form 3^a * 5^b * 7^c.

For the factor to be a odd number a,b,c can take any value as product of 3 odd numbers would always be odd
a can take values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
b can take values 0, 1, 2, 3, 4, 5, 6
and c can take values 0, 1, 2, 3

Total number of odd factor = 10 * 7 * 4 = 280

Correct Option: 5 Best Solution (0)