How many factors of 7721290962 are odd numbers?

M4maths Previous Puzzles

22 Nov 2018 ODD Number

How many factors of 7721290962 are odd numbers?

OPtion

1) 288
2) 360
3) 120
4) 144
5) 150
6) 160
7) 180
8) 240
9) 125
10) None of these

Solution

7721290962 = 31^3 * 17^1 * 11^2 * 7^1 * 3^2 * 2^1

Any factor of this number should be of the form 31^a * 17^b * 11^c * 7^d * 3^e * 2^f

For the factors of this number to be an odd number f should be 0

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

Total number of odd factors = 4*2*3*2*3*1= 144


Option 4)

Correct Option: 4 Best Solution (2)

G.S.Kantharao   5 years AGO

7721290962=2*3^2*7*11^2*17*31^3=2^a*3*^b*7^c*11^d*17^e*31^f
For odd number factors
a=0,b=0,1,2,c=0,1,d=0,1,2,e=0,1,f=0,1,2,3
Number of factors =1*3*2*3*2*4=144
Right option is 4👈

Like? Yes (4) | No (1)  

A.P.Singh   5 years AGO

7721290962= 2* (3^2 * 7 * 11^2 * 17* 31^3)
Number of add factors = 3*2*3*2*4 = 144

Like? Yes (1) | No (1)