How many different primes are in the prime factorization of $87\cdot89\cdot91\cdot93$?
To find the prime factorization of a product of numbers, I can factor each number individually and then combine the factors. For example, $87=3\cdot29$, $89$ is already prime, $91=7\cdot13$, and $93=3\cdot31$. So, the prime factorization of $87\cdot89\cdot91\cdot93$ is $3^2\cdot7\cdot13\cdot29\cdot31\cdot89$. Now, I just need to count how many distinct prime factors there are. I see that there are $6$ different primes: $3, 7, 13, 29, 31,$ and $89$. 