The question in the image asks to "Найдите НОД чисел 728 и 1275," which translates to "Find the GCD (greatest common divisor) of the numbers 728 and 1275."

Step-by-step solution:

We can calculate the GCD using the Euclidean algorithm, which involves repeated division to find the greatest common divisor.

1. Step 1: Divide the larger number by the smaller number and take the remainder. $1275 \div 728 = 1 \quad \text{remainder } 1275 - (728 \times 1) = 547$

2. Step 2: Replace the larger number with the smaller number (728) and the smaller number with the remainder (547). Then repeat the division: $728 \div 547 = 1 \quad \text{remainder } 728 - (547 \times 1) = 181$

3. Step 3: Replace the numbers again. Divide 547 by 181: $547 \div 181 = 3 \quad \text{remainder } 547 - (181 \times 3) = 4$

4. Step 4: Divide 181 by 4: $181 \div 4 = 45 \quad \text{remainder } 181 - (4 \times 45) = 1$

5. Step 5: Divide 4 by 1: $4 \div 1 = 4 \quad \text{remainder } 0$

When the remainder becomes 0, the divisor at this step (1) is the GCD.

Final Answer:

The greatest common divisor (GCD) of 728 and 1275 is 1.

Would you like more details or have questions about the solution? Here are some follow-up questions and a tip:

5 Related Questions:

1. What is the Euclidean algorithm, and how does it work?
2. How can the GCD be used in simplifying fractions?
3. Can GCD calculations be applied to more than two numbers?
4. What is the relationship between GCD and LCM (Least Common Multiple)?
5. What are alternative methods to calculate the GCD (e.g., prime factorization)?

Tip:

If the GCD of two numbers is 1, the numbers are said to be coprime, meaning they have no common divisors other than 1.