Let $n$ be the smallest composite number such that it can be written as the product of two positive integers that differ by 10.  How many distinct prime factors does $n$ have?
The smallest pair of numbers that differ by 10 is 1 and 11; however, they multiply to 11 which is not composite.  We try the next pair up: 2 and 12, which multiply to 24 which is composite, so $n=24$. $24$ factors as $2^3 \cdot 3$, so it has $\boxed{2}$ prime factors: 2 and 3.