M4maths Previous Puzzles

16 Aug 2019 Even Number

How many factors of 8199625500 are even numbers?

OPtion

1) 600
2) 188
3) 144
4) 180
5) 216
6) 288
7) 128
8) 256
9) 96
10) None of these

Solution

8199625500 = 37^2 * 11^3 * 5^3 * 3^2 * 2^2

Any factor of this number should be of the form 37^a * 11^b * 5^c * 3^d * 2^e

For the factor to be an even number e should be non zero.

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

Total number of even factors = 3*4*4*3*2= 288

Option 6)

Correct Option: 6 Best Solution (0)