### Brain Teasers

# Greatest Product

What is the largest product of positive integers whose sum is 20?

### Answer

1458 = 3^6 x 2Three is the smallest number whose product is greater than its sum. Therefore you want to include as many 3's in the answer as possible. Then make 2's (or 4's) out of the remainder.

20 / 3 = 6, remainder 2 so 3^6 x 2

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