Greatest common divisor of 78647 and 77531

To find the greatest common divisor (GCD) of 78647 and 77531, we can use the Euclidean algorithm. Here's how it works:

1. **Divide the larger number by the smaller number and find the remainder.**
2. **Replace the larger number with the smaller number and the smaller number with the remainder.**
3. **Repeat the process until the remainder is 0. The last non-zero remainder is the GCD.**

Let's calculate it step by step:

1. \( 78647 \div 77531 \) gives a quotient of 1 and a remainder of \( 78647 - 77531 \times 1 = 1116 \).
2. \( 77531 \div 1116 \) gives a quotient of 69 and a remainder of \( 77531 - 1116 \times 69 = 77 \).
3. \( 1116 \div 77 \) gives a quotient of 14 and a remainder of \( 1116 - 77 \times 14 = 38 \).
4. \( 77 \div 38 \) gives a quotient of 2 and a remainder of \( 77 - 38 \times 2 = 1 \).
5. \( 38 \div 1 \) gives a quotient of 38 and a remainder of \( 38 - 1 \times 38 = 0 \).

Since the remainder is now 0, the GCD is the last non-zero remainder, which is 1.

So, the greatest common divisor (GCD) of 78647 and 77531 is **1**.

Would you like more details or have any questions about this process?

Here are some related questions that might interest you:

1. What is the Euclidean algorithm?
2. How do you find the least common multiple (LCM) of two numbers?
3. What is the relationship between GCD and LCM?
4. How do you factorize a number into its prime factors?
5. What is the significance of a GCD of 1 between two numbers?
6. How can you determine if two numbers are coprime?
7. What are some practical applications of finding the GCD?
8. How do you extend the Euclidean algorithm to find coefficients in the linear combination?

**Tip:** When two numbers have a GCD of 1, they are said to be relatively prime or coprime, meaning they have no common factors other than 1.

Learn how to find the greatest common divisor (GCD) of 78647 and 77531 using the Euclidean algorithm step-by-step. Understand the concept of GCD and its applications in number theory. Suitable for high school students and beyond.

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