No, the sum of two even numbers is not always divisible by 4.
While it's true that the sum of two even numbers will *always* be an even number, it doesn't guarantee divisibility by 4. Let's explore why using some examples and the given reference.
According to the reference, the sum of two even numbers is *not always divisible by 4*. The reference provides a clear example: 10 + 4 = 14, which is not divisible by 4. The reference further explains that only the sum of *two alternate even numbers* will be divisible by 4.
Here's a breakdown:
- Even Numbers: Even numbers are integers that are exactly divisible by 2 (e.g., 2, 4, 6, 8, 10, 12...).
- Sum of Even Numbers: When you add any two even numbers together, you always get another even number.
- Divisibility by 4: For a number to be divisible by 4, it must be evenly divided by 4 with no remainder (e.g., 4, 8, 12, 16...).
Examples
Let's look at examples to illustrate the point:
| Even Number 1 | Even Number 2 | Sum | Divisible by 4? |
|---|---|---|---|
| 2 | 4 | 6 | No |
| 4 | 6 | 10 | No |
| 6 | 8 | 14 | No |
| 8 | 10 | 18 | No |
| 2 | 6 | 8 | Yes |
| 4 | 8 | 12 | Yes |
As you can see in the table above, some sums of two even numbers are divisible by 4, but most are not.
Key Insights
- The fact that two numbers are even doesn't automatically mean their sum will be a multiple of 4.
- If you add an even number to *itself* or *an adjacent* even number, the sum will *not* be divisible by 4.
- As stated in the reference, only the sum of *two alternate even numbers* (e.g. 2 and 6, 4 and 8) are always divisible by 4.
