### Instruction: How many positive integers, including $1,$ are divisors of both $40$ and $72?$.### Response: So we need to find the number of positive integers that are divisors of both 40 and 72.
Right, so let's list the divisors of 40.
1, 2, 4, 5, 8, 10, 20, and 40.
And the divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Now let's look for divisors that are in both sets.
We see that 1, 2, 4, and 8 are divisors of both 40 and 72.