MathDB

Jane tells you that she is thinking of a three-digit number that is greater than

500

that has exactly

20

positive divisors. If Jane tells you the sum of the positive divisors of her number, you would not be able to figure out her number. If, instead, Jane had told you the sum of the prime divisors of her number, then you also would not have been able to figure out her number. What is Jane's number? (Note: the sum of the prime divisors of

12

2 + 3 = 5

, not

2 + 2 + 3 = 7

Problem Statement