How many factors of 1907980272 are even numbers?

M4maths Previous Puzzles

07 Jun 2018 Even Number

How many factors of 1907980272 are even numbers?

OPtion

1) 360
2) 300
3) 120
4) 90
5) 150
6) 160
7) 180
8) 240
9) 125
10) None of these

Solution

1907980272 = 23^3 * 11^2 * 3^4 * 2^4

Any factor of this number should be of the form 23^a *11^b * 3^c * 2^d

For the factors of this number to be an even number d should be non 0

a can take values 0, 1, 2, 3
b can take values 0, 1, 2
c can take values 0, 1, 2, 3, 4
d can take values 1, 2, 3, 4

Total number of odd factors = 4*3*5*4= 240

Option 8)

Correct Option: 8 Best Solution (0)