When 68 is divided by a certain number, the remainder is 4. Find the sum of all possible divisors.
This brainteaser was supplied by the Mathematical Olympiads for Elementary and Middle Schools (www.moems.org).
Solution: 12 0.
Any number that leaves a remainder of 4 when divided into 68 will have two characteristics:
The factors of 64 greater than 4 are 8, 16, 32 and 64, which have a sum of 8 + 16 + 32 + 64 = 120.
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