what is the greatest whole number that must be a factor of the some of any four consecutive positive odd numbers?

Let's solve this step by step.

### Step 1: Representation of four consecutive odd numbers
Let the four consecutive odd numbers be represented as:
\[
n, n+2, n+4, n+6
\]
where \(n\) is the first odd number.

### Step 2: Sum of the four consecutive odd numbers
The sum of these four numbers is:
\[
n + (n+2) + (n+4) + (n+6)
\]

Simplifying the sum:
\[
n + (n+2) + (n+4) + (n+6) = 4n + 12
\]

### Step 3: Factoring the sum
The expression \(4n + 12\) can be factored as:
\[
4n + 12 = 4(n + 3)
\]

### Step 4: Conclusion
The expression \(4(n + 3)\) shows that the sum of any four consecutive odd numbers is always divisible by 4. Therefore, **4** is the greatest whole number that must be a factor of the sum of any four consecutive odd numbers.

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Would you like more details or have any questions?

Here are some related questions you can explore:
1. What is the sum of the first four consecutive odd numbers?
2. Can the sum of five consecutive odd numbers be divisible by 4?
3. What is the sum of three consecutive odd numbers, and what is its greatest common divisor?
4. How does the sum of consecutive even numbers differ from consecutive odd numbers?
5. If the sum of four consecutive odd numbers is 84, what are the numbers?

**Tip**: When working with sums of sequences, look for patterns or common factors to simplify the problem.

what is the greatest whole number that must be a factor of the sum of any four consecutive positive odd numbers?

Discover how to find the greatest whole number that must be a factor of the sum of any four consecutive odd numbers. This problem explores key algebraic concepts like factoring and number sequences. Suitable for students in Grades 6-8.

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