Question

Найдите НОД каждого примера. !ПОМОГИТЕ СРОЧНО! НОД (128,80) НОД(28,55) НОД(120,15)

Answer 1

Ответ:

НОД(128, 80) = 16

НОД(28,55) = 1

НОД(120,15) = 15

Объяснение:

128 = 2*2*2*2*2*2*2

80 = 2*2*2*2*5

общее - 2*2*2*2, то есть 16

28 = 2*2*7

55 = 11* 5

нет общих множителей, значит 1

120 = 2*2*2*3*5

15 = 3*5

общее - 3*5, то есть 15

Answer 2

Finding the Greatest Common Divisor (GCD)

To find the greatest common divisor (GCD) of each pair, we can use the Euclidean algorithm, which is based on the principle that the GCD of two numbers does not change if the larger number is replaced by its difference with the smaller number.

1. GCD(128, 80): - Applying the Euclidean algorithm: - GCD(128, 80) = GCD(80, 128 % 80) - GCD(80, 48) = GCD(48, 80 % 48) - GCD(48, 32) = GCD(32, 48 % 32) - GCD(32, 16) = GCD(16, 32 % 16) - GCD(16, 0) = 16 - Therefore, the GCD of 128 and 80 is 16.

2. GCD(28, 55): - Applying the Euclidean algorithm: - GCD(55, 28) = GCD(28, 55 % 28) - GCD(28, 27) = GCD(27, 28 % 27) - GCD(27, 1) = GCD(1, 27 % 1) - GCD(1, 0) = 1 - Therefore, the GCD of 28 and 55 is 1.

3. GCD(120, 15): - Applying the Euclidean algorithm: - GCD(120, 15) = GCD(15, 120 % 15) - GCD(15, 0) = 15 - Therefore, the GCD of 120 and 15 is 15.

These are the greatest common divisors for the given pairs.