To determine the smallest number by which 2880 must be divided in order to make it a perfect square, we need to find a number that, when divided into 2880, leaves a perfect square.

Let`s evaluate each option:

Option 1: Divide 2880 by 3. The result is 960, which is not a perfect square.

Option 2: Divide 2880 by 4. The result is 720, which is not a perfect square.

Option 3: Divide 2880 by 5. The result is 576, which is a perfect square (24^2).

Option 4: Divide 2880 by 6. The result is 480, which is not a perfect square.

Therefore, the correct answer is Option 3: 5. By dividing 2880 by 5, we get 576, which is a perfect square, making it the smallest number by which 2880 must be divided to make it a perfect square.