Explanation:

- To find the greatest number that exactly divides 15, 30, and 40, we need their greatest common divisor (GCD).

- Option 1: 3

- 3 divides 15 and 30, but not 40.

- Option 2: 40

- 40 divides itself, but not 15 or 30.

- Option 3: 5

- 5 divides 15, 30, and 40.

- Option 4: 15

- 15 divides itself and 30, but not 40.

The GCD is 5, as it divides all three numbers.

Thus, the greatest number that exactly divides 15, 30, and 40 is 5.