13. The smallest natural number with 10 different factors is
The method to find the number of factors is to first decompose into prime factors, then multiply the exponents plus one. Since $10=1 \times 10=2 \times 5$, the natural number can be expressed as: $a^{9}$ or $a \times b^{4}$, the smallest being $3 \times 2^{4}=48$.