A number is divisible by which of the following if both 2 and 3 can divide it?

A number that is divisible by both 2 and 3 means that it has 2 and 3 as its factors. To determine the correct answer in this scenario, we need to consider what additional factors are generated by the combination of 2 and 3.

When a number is divisible by 2, it is an even number. When it is also divisible by 3, it means that it can be broken down sufficiently to include both of these factors. The least common multiple (LCM) of 2 and 3 is 6.

This means that any number that includes both 2 and 3 as factors must also include their LCM, which is 6. Therefore, if a number can be divided evenly by both 2 and 3, it can also be concluded that it is divisible by 6.

The other options (4, 5, and 8) do not consistently ensure that a number divisible by both 2 and 3 falls under their divisibility requirement, as they either introduce additional factors or do not meet the necessary conditions without the baseline of 2 and 3. Thus, the presence of both 2 and 3 guarantees divisibility by 6, making it the correct