# Prom numbers

A $$b$$-prom number is a positive integer which is the concatenation of the product of its digits and the sum of its digits in base $$b$$. For example, $$3612$$ is a 10-prom number, since the product of its digits is $$36$$ and the sum of its digits is $$12$$, and $$3612$$ is the concatenation of $$36$$ and $$12$$. Note that $$1236$$ is not a 10-prom number; the concatenation must be the product before the sum. Also note that $$01$$ is not a 10-prom number; prom numbers may not begin with $$0$$.

What is the only 3-digit 10-prom number?

×