If c, d and e are consecutive integers, what is cde?

Answer

To solve the problem, we need to find the product of three consecutive integers \(c\), \(d\), and \(e\). Let's go through the solution step by step.

### Step 1: Define the Consecutive Integers
Consecutive integers are integers that follow each other in order. If we let \(c\) be the first integer, then the next two consecutive integers can be defined as:
- \(d = c + 1\)
- \(e = c + 2\)

### Step 2: Write the Product
Now, we can express the product \(cde\) as:
\[ cde = c \times (c + 1) \times (c + 2) \]

### Step 3: Analyze the Product
To analyze the product, we note that among any three consecutive integers, at least one of them must be even. This is because integers alternate between odd and even. Therefore, the product \(cde\) will always include an even number.

### Step 4: Conclusion
Since the product of any number with an even number is always even, we can conclude that:
\[ cde \text{ is an even number.} \]

### Final Answer
Thus, the product \(cde\) of three consecutive integers \(c\), \(d\), and \(e\) is an even number.

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