Calculate the remainder when 6,752,950 is divided by 547.

To calculate the remainder when \( 6,752,950 \) is divided by \( 547 \), we can use the modulo operation:

\[
6,752,950 \mod 547
\]

First, perform the division:

\[
6,752,950 \div 547 \approx 12,344.898
\]

Now, take the integer part of this result:

\[
12,344 \times 547 = 6,752,968
\]

Subtract this result from \( 6,752,950 \):

\[
6,752,950 - 6,752,968 = -18
\]

Since the remainder cannot be negative, we add \( 547 \) to the result:

\[
-18 + 547 = 529
\]

Thus, the remainder when \( 6,752,950 \) is divided by \( 547 \) is \( \boxed{529} \).

Would you like more details on this method or a breakdown of another example?

Here are 5 related questions:
1. What is the remainder when 10,000 is divided by 547?
2. How can you verify your division and remainder calculation using long division?
3. What are some efficient ways to calculate large modulo operations?
4. How does the remainder theorem apply to polynomial division?
5. Can you use modular arithmetic in encryption algorithms like RSA?

**Tip:** When dividing large numbers manually, always check your intermediate calculations by multiplying the quotient back by the divisor!

Find the remainder when 6,752,950 is divided by 547 with this detailed explanation. Learn the modulo operation and how to apply the division algorithm. Suitable for middle school students (Grades 6-8).

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