Splitting 100 coins into piles to maximise product

Divide $100$ pennies into any number of piles of any sizes; your reward is the product of the pile sizes (e.g. piles of $10,20,70$ pay $14000$). The best possible reward can be written as $a\cdot b^c$ with $a$ and $b$ coprime. Compute $abc$.

$384$. Any pile of $5$ or more is beaten by splitting it, and $2+2+2$ is beaten by $3+3$, so the optimum uses as many $3$s as possible. Since $100=32\cdot3+4$, the maximum is $4\cdot3^{32}$, giving $abc=4\cdot3\cdot32=384$.