To determine the largest remainder that can be obtained when an even number is divided by 6, let's analyze the problem step-by-step.
First, recall that an even number is any number that is divisible by 2. Therefore, even numbers can be expressed in the form `2k`, where `k` is an integer.
When an even number `2k` is divided by 6, we are interested in finding the remainder. The possible remainders when any number is divided by 6 are 0, 1, 2, 3, 4, and 5.
Since we are specifically looking at even numbers, the remainder must be an even number as well. Therefore, the possible remainders for an even number could only be 0, 2, or 4, because these are the even numbers within the range of possible remainders.
Now, among these possible even remainders (0, 2, and 4), the largest one is 4. Thus, the largest remainder that can be obtained when an even number is divided by 6 is:
D. 2
Therefore, the correct answer is:
D. 2
