Question

Найдите :1) Нод ( 75,150,225 ) ; 3) Нод ( 81,90,126);2) Нод ( 135,162,270); 4) Нод (45,90,135).

Answer 1

1) НОД(75,150 и 225)=75 (наверное)

Answer 2

Calculating the Greatest Common Divisor (GCD) using Euclidean Algorithm

To find the greatest common divisor (GCD) of the given numbers, we can use the Euclidean Algorithm. This algorithm involves finding the GCD of two numbers and then using that result to find the GCD of the next pair of numbers. Let's calculate the GCD for each set of numbers.

1. GCD of (75, 150, 225): - We start by finding the GCD of 75 and 150. - The GCD of 75 and 150 is 75. - Now, we find the GCD of 75 and 225. - The GCD of 75 and 225 is 75. - Finally, we find the GCD of 75 and 225, which is also 75. - Therefore, the GCD of (75, 150, 225) is 75.

2. GCD of (135, 162, 270): - We start by finding the GCD of 135 and 162. - The GCD of 135 and 162 is 27. - Now, we find the GCD of 27 and 270. - The GCD of 27 and 270 is 27. - Finally, we find the GCD of 27 and 270, which is also 27. - Therefore, the GCD of (135, 162, 270) is 27.

3. GCD of (81, 90, 126): - We start by finding the GCD of 81 and 90. - The GCD of 81 and 90 is 9. - Now, we find the GCD of 9 and 126. - The GCD of 9 and 126 is 9. - Finally, we find the GCD of 9 and 126, which is also 9. - Therefore, the GCD of (81, 90, 126) is 9.

4. GCD of (45, 90, 135): - We start by finding the GCD of 45 and 90. - The GCD of 45 and 90 is 45. - Now, we find the GCD of 45 and 135. - The GCD of 45 and 135 is 45. - Finally, we find the GCD of 45 and 135, which is also 45. - Therefore, the GCD of (45, 90, 135) is 45.

The GCD for each set of numbers has been calculated using the Euclidean Algorithm.