BRUTE FORCE YA YEET divisors of 500, lets list them
1 and 500
2 and 250
4 and 125
5 and 100
10 and 50
20 and 25
we get 25 and 20 next, which means that its just a repeated list, so the numbers above are the positive divisors.
Lets add them now.
1+2+4+5+10+20+500+250+125+100+50+25 = 1092
Lets prime factorize 1092
1092
4 * 273
22 * 21 * 13
22 * 7 * 3 * 13
so the distinct prime divisors are 2 + 7 + 3 + 13 = 25