Question

Difference between the total number of even and odd factors of 882000, is

Answer 1

Given:

Given number = 882000

To Find:

Difference between the total number of even and odd factors.

Solution:

Calculate the prime factors of 882000;

$882000=2^4$×$3^2$×$5^3$×$7^2$

Total factors= $(4+1)(2+1)(3+1)(2+1)$

                    =$5.3.4.3$

                    =$180$

Total odd factors =$(0+1)((2+1)(3+1)(2+1)$

                             =$1.3.4.3$

                             =$36$

Total even factors= total factors- total odd factors

                             = $180-36$

                             =$144$

Difference of even factors and odd factors= $144-36$

                                                                       =$108$

Hence the difference between even and odd factors is 108.

Answer 2

Given:

Given number = 882000

To Find:

Difference between the total number of even and odd factors.

Solution:

Calculate the prime factors of 882000;

$882000 =2^{4}*3^{2}*5^{3}*7^{2}$

Total factors= $(4+1)(2+1)(3+1)(2+1)=5*3*4*3$

                     = $180$

Total odd factors = $(0+1)(2+1)(3+1)(2+1)=1*3*4*3=36$

Total even factors= total factors- total odd factors

                               = $180-36=144$

Difference of even factors and odd factors= $144-36=108$

Hence the difference between even and odd factors is 108.

#SPJ3