Question

find the sum of even positive divisors of 10000​

Answer 1

Answer:

2184

Step-by-step explanation:

Let n is a positive even divisor of 1000 if and only if n=2m,

where m is a divisor of 500.

Since 500=22×53,

there are (2+1)(3+1)=12 divisors of 500.

Those divisors are

1,2,4,5,10,20,500,250,125,100,50,25

so there are 12 positive even divisors of 1000.

Those divisors are

2,4,8,10,20,40,1000,500,250,200,100,

50

The sum of the positive divisors of 500=2^2×5^3 equals

(2^3−1)/(2−1)×(5^4−1)/(5−1)=1092

So the sum of the even divisors of 1000 is 2×1092=2184