How many factors of 4412166264 are perfect squares?

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20 Jun 2019 Perfect Square

How many factors of 4412166264 are perfect squares?

OPtion

1) 36
2) 16
3) 12
4) 32
5) 15
6) 30
7) 18
8) 24
9) 27
10) None of these

Solution

4412166264 = 31^3 * 17^1 * 11^2 * 3^2 * 2^3

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

For the factor to be a perfect square a,b,c,d,e have to be even.

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


Total number of perfect squares = 2*1*2*2*2 = 16

Option 2)

Correct Option: 2 Best Solution (5)

G.S.Kantharao   4 years AGO

4412166264=2^3*3^2*11^2*17*31^3
Perfect Squares to be
=2*2*2*2 (From 2^2*3^2*11^2*31^2)=16
So my option is 2👈

Like? Yes (3) | No   

Varun   4 years AGO

Given = 2^3*3^2*11^2*17*31^3
2 3 11 31 have repeated factor, that can make perfect squares
So we can have 2*2*2*2 factors
= 16

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RAMADURAI NATESAN   4 years AGO

Given number = 2^3*3^2*11^2*17^1*31^3
Any factor of this no. should be in the form of
2^a*3^b*11^c*17^d*31^e.
For the factor to be perfect square,a,b,c,d,e shd be even
Following are the possibilities ;
a=0,2. b=0,2. c=0,2. d=0 and e=0,2
Total no.of factors that can be perfect squares is=
2*2*2*1*2 = 16

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SAYAN CHATTERJEE   4 years AGO

4412166264= 2^3*3^2*11^2*17^1*31^2
So, the nos are (2*2*2*1*2)=16.
Option 2.

Like? Yes | No (1)  

AASHRAY AJAY SHARMA   4 years AGO

Factors of the number is (2^3) * (3^2) * (11^2) * (17) * (31^3)

For any perfect square, all the powers of the primes have to be even numbers.
Any factor of this number should be of the form 2^a * 3^b * 7^c*11^d*31^e
For the factor to be a perfect square a,b,c have to be even.
a can take values 0, 2.
b can take values 0, 2
c can take values 0, 2
d can take values 0
e can take values 0,2
Total number of perfect squares = 2*2*2*1*2 = 16 (Option 2)

Like? Yes | No (1)