The sum of 3 consecutive even numbers is always divisible by :

Options

A. 24
B. 48
C. 10
D. none of these

Answer

To solve the problem of finding out by what number the sum of three consecutive even numbers is always divisible, we can follow these steps:

### Step 1: Define the first even number
Let the first even number be represented as \( x \).

### Step 2: Identify the next two consecutive even numbers
The second consecutive even number can be expressed as \( x + 2 \), and the third consecutive even number can be expressed as \( x + 4 \).

### Step 3: Write the sum of the three consecutive even numbers
Now, we can write the sum of these three even numbers:
\[ \text{Sum} = x + (x + 2) + (x + 4) \]

### Step 4: Simplify the sum
Combining the terms, we get:
\[ \text{Sum} = x + x + 2 + x + 4 = 3x + 6 \]

### Step 5: Factor the sum
We can factor out a common factor from the sum:
\[ \text{Sum} = 3(x + 2) \]

### Step 6: Analyze the divisibility
From the expression \( 3(x + 2) \), we can see that the sum is always divisible by 3, regardless of the value of \( x \).

### Conclusion
Since the sum of three consecutive even numbers is \( 3(x + 2) \), it is always divisible by 3. However, none of the provided options (24, 48, 10) are divisible by 3, so the correct answer is "none of these."