Question

НОД 6 И 13 ,НОД 14 И 18,НОД 28 И 42 21 И 33 15 42 И 105 21 28 И 35

Answer 1

Ответ:

НОД(6, 13) = 1

НОД(14, 18) = 2

НОД(28, 42) = 2•7 = 14

НОД(21, 33) = 3

НОД(15, 42, 105) = 3

НОД(21, 28, 35) = 7

Answer 2

To find the greatest common divisor (GCD) of two numbers, you can use the Euclidean algorithm. I'll calculate the GCD for the given pairs of numbers:

1. GCD(6, 13): Using the Euclidean algorithm: 13 = 2 * 6 + 1 6 = 6 * 1 + 0 The remainder becomes 0, so the GCD is 1.

2. GCD(14, 18): Using the Euclidean algorithm: 18 = 1 * 14 + 4 14 = 3 * 4 + 2 4 = 2 * 2 + 0 The remainder becomes 0, so the GCD is 2.

3. GCD(28, 42): Using the Euclidean algorithm: 42 = 1 * 28 + 14 28 = 2 * 14 + 0 The remainder becomes 0, so the GCD is 14.

4. GCD(21, 33): Using the Euclidean algorithm: 33 = 1 * 21 + 12 21 = 1 * 12 + 9 12 = 1 * 9 + 3 9 = 3 * 3 + 0 The remainder becomes 0, so the GCD is 3.

5. GCD(15, 42): Using the Euclidean algorithm: 42 = 2 * 15 + 12 15 = 1 * 12 + 3 12 = 4 * 3 + 0 The remainder becomes 0, so the GCD is 3.

6. GCD(28, 35): Using the Euclidean algorithm: 35 = 1 * 28 + 7 28 = 4 * 7 + 0 The remainder becomes 0, so the GCD is 7.

Therefore, the GCDs for the given pairs of numbers are:

1. GCD(6, 13) = 1
2. GCD(14, 18) = 2
3. GCD(28, 42) = 14
4. GCD(21, 33) = 3
5. GCD(15, 42) = 3
6. GCD(28, 35) = 7