To determine which pairs of numbers are relatively prime, we need to identify pairs of numbers that have no common factors other than 1.
Here’s a step-by-step breakdown for each pair of numbers:
1. 9 and 15:
- Factors of 9: {1, 3, 9}
- Factors of 15: {1, 3, 5, 15}
- Common factors: {1, 3}
- Since the common factors include 3, 9 and 15 are not relatively prime.
2. 9 and 40:
- Factors of 9: {1, 3, 9}
- Factors of 40: {1, 2, 4, 5, 8, 10, 20, 40}
- Common factors: {1}
- The only common factor is 1, so 9 and 40 are relatively prime.
3. 9 and 21:
- Factors of 9: {1, 3, 9}
- Factors of 21: {1, 3, 7, 21}
- Common factors: {1, 3}
- Since the common factors include 3, 9 and 21 are not relatively prime.
4. 15 and 21:
- Factors of 15: {1, 3, 5, 15}
- Factors of 21: {1, 3, 7, 21}
- Common factors: {1, 3}
- Since the common factors include 3, 15 and 21 are not relatively prime.
5. 21 and 40:
- Factors of 21: {1, 3, 7, 21}
- Factors of 40: {1, 2, 4, 5, 8, 10, 20, 40}
- Common factors: {1}
- The only common factor is 1, so 21 and 40 are relatively prime.
Therefore, the pairs of numbers that are relatively prime are:
- 9 and 40
- 21 and 40
