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Coin Bundle

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Parts

Part 1

You are given a pile of 100 coins. You may arrange these coins into however many stacks you want and you may put as many coins into each stack as you would like. Your payout would be the product of the number of coins among all of the stacks.

For example, if you make three stacks of sizes 20, 20, and 60, your payout is 20 x 20 x 60 = 24000 . The optimal arrangement of the coins will give you a payout of $a * b^c$, where $a$ and $b$ are relatively prime. Find $a$, $b$ and $c$.