jmc

We can first find the prime factorization of $23,232$, which is $2^6\cdot 3^1\cdot 11^2$. Now, we add one to our powers and multiply. Therefore, the answer is $(6+1)\cdot (1+1)\cdot (2+1)=7\cdot 2\cdot 3=\boxed{42}$ Note: 23232 is a large number, so we can look for shortcuts to factor it. One way to factor it quickly is to use 3 and 11 divisibility rules to observe that $23232=3\cdot 7744=3\cdot 11\cdot 704=3\cdot 11^2\cdot 64=3^1\cdot 11^2\cdot 2^6$. Another way is to spot the "32" and compute that $23232=32\cdot (101+10000/16)=32\cdot (101+5^4)=32\cdot 726=32\cdot 11\cdot 66$.