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

Options

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

Answer

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

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

**Hint:** Remember that consecutive even numbers differ by 2.

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

**Hint:** This equation represents the relationship between the two numbers and their product.

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

**Hint:** Make sure to distribute correctly when expanding the equation.

### Step 4: Rearrange the Equation
To form a standard quadratic equation, we rearrange it:
\[ x^2 + 2x - 624 = 0 \]

**Hint:** A quadratic equation is typically in the form \( ax^2 + bx + c = 0 \).

### 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 up to \(2\). The numbers that satisfy this are \(26\) and \(-24\). Thus, we can rewrite the equation as:
\[ (x + 26)(x - 24) = 0 \]

**Hint:** The factors should give you the product of the constant term and the sum of the linear coefficient.

### Step 6: Solve for \( x \)
Setting each factor to zero gives us:
1. \( x + 26 = 0 \) → \( x = -26 \) (not valid since we need positive even numbers)
2. \( x - 24 = 0 \) → \( x = 24 \)

**Hint:** Since we are looking for even numbers, we discard negative solutions.

### Step 7: Find the Consecutive Even Number
Now that we have \( x = 24 \), the next consecutive even number is:
\[ x + 2 = 24 + 2 = 26 \]

**Hint:** Always check if the numbers you found are indeed consecutive even numbers.

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

**Final Answer:** One of the numbers is **24**.