The ratio \( 45:6544 \) can be simplified by finding the greatest common divisor (GCD) of 45 and 6544 and dividing both terms by this GCD.

Let's calculate the GCD first.

#### GCD of 45 and 6544:
- Prime factorization of 45 = \( 3^2 \times 5 \)
- Prime factorization of 6544 = \( 2^4 \times 409 \)

There are no common factors between 45 and 6544, so the GCD is 1.

This means the ratio \( 45:6544 \) is already in its simplest form.

The simplified ratio is:
\[ 45:6544 \]

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What is a ratio, and how is it different from a fraction?
2. How do you simplify ratios that share common factors?
3. How is the GCD used in reducing ratios?
4. Can the ratio \( 45:6544 \) be expressed as a decimal or percentage?
5. How are ratios used in real-life applications like scaling or proportions?

**Tip:** Ratios can often be written in fraction form to help visualize their relationship more clearly!

Learn how to simplify the ratio 45:6544 using the Greatest Common Divisor (GCD). This detailed explanation covers the key mathematical concepts of ratios, prime factorization, and GCD, making it ideal for students in Grades 6-8.

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