設 \(\displaystyle 15!=2^a3^b5^c\cdot n\)，其中 \(n\) 沒有 \(2,3,5\) 的因數，
且令 \(\left[x\right]=\)不超過 \(x\) 的最大整數值，則
\(\displaystyle a=\left[\frac{15}{2}\right]+\left[\frac{15}{2^2}\right]+\left[\frac{15}{2^3}\right]+\left[\frac{15}{2^4}\right]+\cdots=11,\)
\(\displaystyle b=\left[\frac{15}{3}\right]+\left[\frac{15}{3^2}\right]+\left[\frac{15}{3^3}\right]+\left[\frac{15}{3^4}\right]+\cdots=6,\)
\(\displaystyle c=\left[\frac{15}{5}\right]+\left[\frac{15}{5^2}\right]+\left[\frac{15}{5^3}\right]+\left[\frac{15}{5^4}\right]+\cdots=3,\)
所以，\(\displaystyle 15!=10^3\cdot\left(2^8\cdot3^6\cdot n\right)=12^5\cdot\left(2\cdot 5^3\cdot n\right),\)
\(\displaystyle \Rightarrow h=3,k=5 \Rightarrow h+k=8.\)
