The common divisors of 16 and 40 are: 1, 2, 4, and 8.

To find all common divisors, we need to find the factors of each number and compare them.

16 can be written as 2 x 2 x 2 x 2 and 40 can be written as 2 x 2 x 2 x 5.

Therefore, the common divisors are the common factors of 16 and 40, which are 2 and 2 x 2 = 4.

In other words, the common divisors are the numbers that evenly divide both 16 and 40 without any remainder.

So, to find all the common divisors, we can create a list of factors for both numbers and then find the numbers that appear in both lists.

Thus, all the common divisors of 16 and 40 are 1, 2, 4, and 8.