Question

Используя предыдущее задание,найдите:НОД(12,42),НОД(12,54),НОД(18,30),НОД(12,75),НОД(12,45),НОД(12,36),НОД(18,54) ДЛЯ 5 КЛАССОВ ПОМОГИТЕ ОЧЕНЬ НАДО ПЛИЗ

Answer 1

НОД(12,42)=6
НОД(12,54)=6
НОД(18,30)=6
НОД(12,75)=3
НОД(12,45)=3
НОД(12,36)=12
НОД(18,54)=18

Answer 2

НОД(12, 42)

To find the greatest common divisor (НОД) of 12 and 42, we can use the Euclidean algorithm. The Euclidean algorithm states that the НОД of two numbers can be found by repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is zero. The last non-zero remainder is the НОД of the two numbers.

Let's apply the Euclidean algorithm to find the НОД(12, 42):

1. Divide 42 by 12: 42 ÷ 12 = 3 remainder 6 2. Divide 12 by 6: 12 ÷ 6 = 2 remainder 0

Since the remainder is now zero, the НОД(12, 42) is the last non-zero remainder, which is 6.

НОД(12, 42) = 6.

НОД(12, 54)

To find the НОД(12, 54), let's apply the Euclidean algorithm:

1. Divide 54 by 12: 54 ÷ 12 = 4 remainder 6 2. Divide 12 by 6: 12 ÷ 6 = 2 remainder 0

The last non-zero remainder is 6, so НОД(12, 54) = 6.

НОД(18, 30)

To find the НОД(18, 30), let's apply the Euclidean algorithm:

1. Divide 30 by 18: 30 ÷ 18 = 1 remainder 12 2. Divide 18 by 12: 18 ÷ 12 = 1 remainder 6 3. Divide 12 by 6: 12 ÷ 6 = 2 remainder 0

The last non-zero remainder is 6, so НОД(18, 30) = 6.

НОД(12, 75)

To find the НОД(12, 75), let's apply the Euclidean algorithm:

1. Divide 75 by 12: 75 ÷ 12 = 6 remainder 3 2. Divide 12 by 3: 12 ÷ 3 = 4 remainder 0

The last non-zero remainder is 3, so НОД(12, 75) = 3.

НОД(12, 45)

To find the НОД(12, 45), let's apply the Euclidean algorithm:

1. Divide 45 by 12: 45 ÷ 12 = 3 remainder 9 2. Divide 12 by 9: 12 ÷ 9 = 1 remainder 3 3. Divide 9 by 3: 9 ÷ 3 = 3 remainder 0

The last non-zero remainder is 3, so НОД(12, 45) = 3.

НОД(12, 36)

To find the НОД(12, 36), let's apply the Euclidean algorithm:

1. Divide 36 by 12: 36 ÷ 12 = 3 remainder 0

Since the remainder is now zero, the НОД(12, 36) is the last non-zero remainder, which is 12.

НОД(12, 36) = 12.

НОД(18, 54)

To find the НОД(18, 54), let's apply the Euclidean algorithm:

1. Divide 54 by 18: 54 ÷ 18 = 3 remainder 0

Since the remainder is now zero, the НОД(18, 54) is the last non-zero remainder, which is 18.

НОД(18, 54) = 18.

I hope this helps! Let me know if you have any further questions.