Question

нок 12 и 21, 15 и 21,12 и 27,15 и 27.нод17 и 68,34 и 68,17 и 102,34 и 102.

Answer 1

Среди чисел 12, 15, 25, 35 и 49

Answer 2

Finding the Greatest Common Divisor (GCD)

To find the greatest common divisor (GCD) of the given pairs of numbers, we can use the Euclidean algorithm. The Euclidean algorithm 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.

Let's calculate the GCD for each pair of numbers:

1. GCD of 12 and 21: - Using the Euclidean algorithm: - GCD(12, 21) = GCD(21, 12) = GCD(9, 12) = GCD(12, 9) = GCD(3, 9) = GCD(9, 3) = 3 - Therefore, the GCD of 12 and 21 is 3.

2. GCD of 15 and 21: - Using the Euclidean algorithm: - GCD(15, 21) = GCD(21, 15) = GCD(6, 15) = GCD(15, 6) = GCD(3, 6) = GCD(6, 3) = 3 - Therefore, the GCD of 15 and 21 is 3.

3. GCD of 12 and 27: - Using the Euclidean algorithm: - GCD(12, 27) = GCD(27, 12) = GCD(15, 12) = GCD(12, 15) = GCD(3, 15) = GCD(15, 3) = 3 - Therefore, the GCD of 12 and 27 is 3.

4. GCD of 15 and 27: - Using the Euclidean algorithm: - GCD(15, 27) = GCD(27, 15) = GCD(12, 15) = GCD(15, 12) = GCD(3, 12) = GCD(12, 3) = 3 - Therefore, the GCD of 15 and 27 is 3.

5. GCD of 17 and 68: - Using the Euclidean algorithm: - GCD(17, 68) = GCD(68, 17) = GCD(34, 17) = GCD(17, 34) = GCD(17, 17) = 17 - Therefore, the GCD of 17 and 68 is 17.

6. GCD of 34 and 68: - Using the Euclidean algorithm: - GCD(34, 68) = GCD(68, 34) = GCD(34, 34) = 34 - Therefore, the GCD of 34 and 68 is 34.

7. GCD of 17 and 102: - Using the Euclidean algorithm: - GCD(17, 102) = GCD(102, 17) = GCD(85, 17) = GCD(17, 85) = GCD(17, 51) = GCD(51, 17) = 17 - Therefore, the GCD of 17 and 102 is 17.

8. GCD of 34 and 102: - Using the Euclidean algorithm: - GCD(34, 102) = GCD(102, 34) = GCD(34, 34) = 34 - Therefore, the GCD of 34 and 102 is 34.

In summary, the greatest common divisors (GCDs) for the given pairs of numbers are: - 12 and 21: 3 - 15 and 21: 3 - 12 and 27: 3 - 15 and 27: 3 - 17 and 68: 17 - 34 and 68: 34 - 17 and 102: 17 - 34 and 102: 34