How many factors of 997972488 are even numbers?

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01 Mar 2019 Even Number

How many factors of 997972488 are even numbers?

OPtion

1) 125
2) 75
3) 120
4) 135
5) 60
6) 75
7) 180
8) 150
9) 90
10) None of these

Solution

997972488 = 73^2 * 17^2 * 3^4 * 2^3

Any factor of this number should be of the form 73^a * 17^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
b can take values 0, 1, 2
c can take values 0, 1, 2, 3, 4
d can take values 1, 2, 3


Total number of odd factors = 3*3*5*3= 135



Option 4)

Correct Option: 4 Best Solution (1)

Varun   5 years AGO

997972488 = 2^3 * 3^4 * 17^2 * 73*2
Total factors = (3+1)* (4+1) * (2+1) * (2+1)
= 4 * 5 * 3 * 3 = 180
Odd factors will not have 2 as factor so product will be 5 * 3 * 3 = 45
So even factors = 180-45 = 135
= Option (4)

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