When 731+732+783 +734 is divided by 175, the remainder is:

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To find the remainder when the sum \(731 + 732 + 733 + 734\) is divided by 175, follow these steps:

1. **Calculate the sum:**
   \[
   731 + 732 + 733 + 734 = 2930
   \]

2. **Divide the sum by 175:**
   \[
   \frac{2930}{175} \approx 16.74
   \]

   The quotient is 16, and the remainder is calculated as:
   \[
   2930 - (175 \times 16) = 2930 - 2800 = 130
   \]

Therefore, the remainder when \(731 + 732 + 733 + 734\) is divided by 175 is **130**.

Since the options you provided (2, 8, 3, 8, 4, 8) do not include 130, it seems there may have been a misunderstanding. Double-check if there's another way the problem is meant to be interpreted or if the options listed were input incorrectly. 

Would you like to explore this problem further or ask a different question? Here are some related questions:

1. What is modular arithmetic and how is it applied in such problems?
2. How can you verify the remainder using a calculator?
3. What are the properties of divisibility relevant to this problem?
4. How to solve similar problems involving larger numbers?
5. What are common mistakes to avoid in remainder problems?
6. How would the process differ if dividing by another number?
7. What is the importance of remainders in number theory?
8. How does the modulo operation work in programming?

**Tip:** Double-check the sum and division process to ensure accurate calculation of the remainder.

Learn how to find the remainder when the sum of numbers (731, 732, 733, 734) is divided by 175 with a step-by-step solution. This problem involves modular arithmetic and the remainder theorem. Suitable for high school students studying number systems.

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