Question

Какие пары, составленные из чисел 12,19,21,15,16,34являются взаимно простыми числами?

Answer 1

Надеюсь ответ правильный:19 и 34

Answer 2

Checking for Relatively Prime Pairs

To determine which pairs of numbers are relatively prime, we need to check if their greatest common divisor (GCD) is 1. Let's examine the pairs of numbers provided and determine which ones are relatively prime.

1. Pair 1: 12 and 19 2. Pair 2: 12 and 21 3. Pair 3: 12 and 15 4. Pair 4: 12 and 16 5. Pair 5: 12 and 34 6. Pair 6: 19 and 21 7. Pair 7: 19 and 15 8. Pair 8: 19 and 16 9. Pair 9: 19 and 34 10. Pair 10: 21 and 15 11. Pair 11: 21 and 16 12. Pair 12: 21 and 34 13. Pair 13: 15 and 16 14. Pair 14: 15 and 34 15. Pair 15: 16 and 34

Let's calculate the GCD for each pair to determine which ones are relatively prime.

Calculating the GCD

The GCD can be calculated using various methods, such as the Euclidean algorithm. Let's calculate the GCD for each pair of numbers.

1. Pair 1: 12 and 19 - GCD(12, 19) = 1 - This pair is relatively prime.

2. Pair 2: 12 and 21 - GCD(12, 21) = 3 - This pair is not relatively prime.

3. Pair 3: 12 and 15 - GCD(12, 15) = 3 - This pair is not relatively prime.

4. Pair 4: 12 and 16 - GCD(12, 16) = 4 - This pair is not relatively prime.

5. Pair 5: 12 and 34 - GCD(12, 34) = 2 - This pair is not relatively prime.

6. Pair 6: 19 and 21 - GCD(19, 21) = 1 - This pair is relatively prime.

7. Pair 7: 19 and 15 - GCD(19, 15) = 1 - This pair is relatively prime.

8. Pair 8: 19 and 16 - GCD(19, 16) = 1 - This pair is relatively prime.

9. Pair 9: 19 and 34 - GCD(19, 34) = 1 - This pair is relatively prime.

10. Pair 10: 21 and 15 - GCD(21, 15) = 3 - This pair is not relatively prime.

11. Pair 11: 21 and 16 - GCD(21, 16) = 1 - This pair is relatively prime.

12. Pair 12: 21 and 34 - GCD(21, 34) = 1 - This pair is relatively prime.

13. Pair 13: 15 and 16 - GCD(15, 16) = 1 - This pair is relatively prime.

14. Pair 14: 15 and 34 - GCD(15, 34) = 1 - This pair is relatively prime.

15. Pair 15: 16 and 34 - GCD(16, 34) = 2 - This pair is not relatively prime.

Summary

Based on the calculations, the pairs of numbers that are relatively prime are: - 12 and 19 - 19 and 21 - 19 and 15 - 19 and 16 - 19 and 34 - 21 and 16 - 21 and 34 - 15 and 16 - 15 and 34

These pairs have a GCD of 1, indicating that they are relatively prime.