jmc

By listing all the positive integer divisors of 100, we find that the requested product is $1\times 2\times 4\times 5\times 10\times 20\times 25\times 50\times 100$. Pair 1 with 100, 2 with 50, 4 with 25, and 5 with 20 to obtain 4 factors of 100, leaving one more factor of 10. In total, the product is $(100^4)(10)=10^9=\boxed{1,000,000,000}$. Notice that this method may be generalized to show that for all positive integers $n$, the product of the the positive integer divisors of $n$ is $n^{d/2}$ where $d$ is the number of divisors of $n$.