M4maths Previous Puzzles

29 Aug 2018 Even Number

How many factors of 45434373264 are even numbers?

OPtion

1) 288
2) 360
3) 420
4) 432
5) 384
6) 360
7) 192
8) 240
9) 396
10) None of these

Solution

45434373264 = 89^1* 31^3 * 17^1 * 7^1 * 3^2 * 2^4

Any factor of this number should be of the form 31^a * 17^b * 7^c * 3^d * 2^e * 89 ^f

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

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

Total number of even factors = 4*2*2*3*4*2= 384

Option 5)

Correct Option: 5 Best Solution (1)

Varun   6 years AGO

Significant factors are 2 2 2 2 2
So, it contributes to even factors along with 3 3 7 17 31 31 31 and 89
So total 384
= Option (5)

Like? Yes (1) | No