How many factors of 3622184564625 are odd numbers?

M4maths Previous Puzzles

28 Dec 2018 ODD Number

How many factors of 3622184564625 are odd numbers?

OPtion

1) 600
2) 188
3) 144
4) 180
5) 288
6) 576
7) 128
8) 256
9) 96
10) None of these

Solution

3622184564625 = 37^2 * 19^1 * 11^3 * 5^3 * 3^2 * 31^1

Any factor of this number should be of the form 37^a * 19^b * 11^c * 5^d * 3^e * 31^f

All the factors of this number would be an odd number as there is no even factor

a can take values 0, 1, 2
b can take values 0, 1,
c can take values 0, 1, 2, 3
d can take values 0, 1, 2, 3
e can take values 0, 1, 2, 3
and f can take value 0, 1

Total number of odd factors = 3*2*4*4*4*2= 768

Option 10)

Correct Option: 10 Best Solution (0)