How many positive divisors does the number $24$ have?
I can start by dividing by $2$, the smallest prime number, and see how many times it goes into $24$. $24 \div 2 = 12$, so $2$ is a factor. I can divide $12$ by $2$ again, and get $6$. I can divide $6$ by $2$ one more time, and get $3$. Now I have $3$, which is also a prime number, and I cannot divide it by $2$ anymore. So the prime factorization of $24$ is $2^3 \times 3^1$. The formula is to add one to each exponent and multiply them together. So the number of positive divisors of $24$ is $(3 + 1) \times (1 + 1) = 4 \times 2 = 8$. 