Question

НОД (123;567)Помогите!

Answer 1

Решение задания приложено

Answer 2

Разложим числа на простые множители и найдем общие множители чисел:
123 = 3 · 41
567 = 3 · 3 · 3 · 3 · 7
Общие множители чисел: 3
НОД (123; 567) = 3

Answer 3

To find the greatest common divisor (GCD) of two numbers, 123 and 567, you can use the Euclidean algorithm. The Euclidean algorithm is a simple and efficient method for finding the GCD of two integers.

Here are the steps to find the GCD of 123 and 567:

Step 1: Divide the larger number by the smaller number. Step 2: Take the remainder of the division. Step 3: Replace the larger number with the smaller number and the smaller number with the remainder. Step 4: Repeat steps 1 to 3 until the remainder becomes zero. Step 5: The last non-zero remainder is the GCD of the two original numbers.

Let's calculate it step by step:

Step 1: Divide 567 by 123 567 ÷ 123 = 4 with a remainder of 81

Step 2: Replace 567 with 123 and 123 with 81

Step 3: Divide 123 by 81 123 ÷ 81 = 1 with a remainder of 42

Step 4: Replace 123 with 81 and 81 with 42

Step 5: Divide 81 by 42 81 ÷ 42 = 1 with a remainder of 39

Step 6: Replace 81 with 42 and 42 with 39

Step 7: Divide 42 by 39 42 ÷ 39 = 1 with a remainder of 3

Step 8: Replace 42 with 39 and 39 with 3

Step 9: Divide 39 by 3 39 ÷ 3 = 13 with a remainder of 0

Since the remainder has become zero, we stop here. The last non-zero remainder was 3. Therefore, the greatest common divisor (GCD) of 123 and 567 is 3.

So, GCD(123, 567) = 3