The number $1341$ can be written as the sum of three consecutive positive integers. What is the largest of these integers?

Let's denote the three consecutive positive integers as $ x - 1 $, $ x $, and $ x + 1 $.

The sum of these three integers is:
\[
(x - 1) + x + (x + 1) = 3x
\]

We are told that this sum equals 1341:
\[
3x = 1341
\]

Now, solve for $ x $:
\[
x = \frac{1341}{3} = 447
\]

So, the three consecutive integers are $ 446 $, $ 447 $, and $ 448 $.

The largest of these integers is $ \boxed{448} $.

Would you like to explore any details or ask questions? Here are some related problems:

1. What if the number was 2022 instead of 1341? What would be the largest integer then?
2. Can you find a formula for the largest integer in terms of the sum $ S $ for three consecutive numbers?
3. How does the problem change if we use four consecutive integers instead of three?
4. What if one of the integers is a multiple of 5? How would that affect the solution?
5. How do we generalize this method for finding the largest number when given any odd number of consecutive integers?

**Tip:** When dealing with sums of consecutive integers, expressing them around a central term simplifies the arithmetic and ensures the problem is balanced.

Learn how to find the largest integer in a series of three consecutive positive integers that sum up to 1341. This problem involves arithmetic sequences and is suitable for students in Grades 7-9.

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