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2015 E14
2015 E14
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MBMT Team Rounds
Problems
(1)
MBMT Team -- Euler #14
Source:
3/29/2015
Jane tells you that she is thinking of a three-digit number that is greater than
500
500
500
that has exactly
20
20
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
12
12
is
2
+
3
=
5
2 + 3 = 5
2
+
3
=
5
, not
2
+
2
+
3
=
7
2 + 2 + 3 = 7
2
+
2
+
3
=
7
.)