The product of two consecutive even numbers is 624 then one of the number is :

Options

A. 13
B. 25
C. 26
D. 28

Answer

To solve the problem of finding two consecutive even numbers whose product is 624, we can follow these steps:

### Step 1: Define the numbers
Let the first even number be \( x \). Since we are looking for consecutive even numbers, the next even number will be \( x + 2 \).

### Step 2: Set up the equation
According to the problem, the product of these two consecutive even numbers is 624. Therefore, we can write the equation:
\[ x(x + 2) = 624 \]

### Step 3: Expand the equation
Expanding the left side of the equation gives us:
\[ x^2 + 2x = 624 \]

### Step 4: Rearrange the equation
To solve for \( x \), we can rearrange the equation to set it to zero:
\[ x^2 + 2x - 624 = 0 \]

### Step 5: Factor the quadratic equation
Next, we need to factor the quadratic equation. We are looking for two numbers that multiply to -624 and add to 2. The numbers that satisfy this condition are 26 and -24. Thus, we can factor the equation as:
\[ (x + 26)(x - 24) = 0 \]

### Step 6: Solve for \( x \)
Setting each factor equal to zero gives us:
1. \( x + 26 = 0 \) → \( x = -26 \) (not a valid even number in this context)
2. \( x - 24 = 0 \) → \( x = 24 \)

### Step 7: Find the consecutive even numbers
Now that we have \( x = 24 \), the consecutive even numbers are:
- First number: \( 24 \)
- Second number: \( 24 + 2 = 26 \)

### Conclusion
Thus, one of the consecutive even numbers is **24** and the other is **26**.