To solve the problem of forming 12 pairs of numbers from the list {2, 4, 7, 9, 10, 12, 15, 22} that are not co-prime, we need to identify pairs that share a common factor greater than 1. Here’s a step-by-step solution:
### Step 1: Understand Co-prime Numbers
Co-prime numbers are pairs of numbers that have no common factors other than 1. This means their greatest common divisor (GCD) is 1.
### Step 2: Identify Common Factors
We will look for pairs of numbers from the given list that share common factors greater than 1.
### Step 3: List the Numbers
The numbers provided are: 2, 4, 7, 9, 10, 12, 15, 22.
### Step 4: Find Pairs
We will create pairs from the list and check if they are not co-prime by finding their common factors.
1. **Pair (4, 10)**:
- Factors of 4: 1, 2, 4
- Factors of 10: 1, 2, 5, 10
- Common factor: 2 (not co-prime)
2. **Pair (4, 12)**:
- Factors of 4: 1, 2, 4
- Factors of 12: 1, 2, 3, 4, 6, 12
- Common factor: 2 (not co-prime)
3. **Pair (4, 22)**:
- Factors of 4: 1, 2, 4
- Factors of 22: 1, 2, 11, 22
- Common factor: 2 (not co-prime)
4. **Pair (9, 15)**:
- Factors of 9: 1, 3, 9
- Factors of 15: 1, 3, 5, 15
- Common factor: 3 (not co-prime)
5. **Pair (10, 12)**:
- Factors of 10: 1, 2, 5, 10
- Factors of 12: 1, 2, 3, 4, 6, 12
- Common factor: 2 (not co-prime)
6. **Pair (10, 22)**:
- Factors of 10: 1, 2, 5, 10
- Factors of 22: 1, 2, 11, 22
- Common factor: 2 (not co-prime)
7. **Pair (12, 22)**:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 22: 1, 2, 11, 22
- Common factor: 2 (not co-prime)
8. **Pair (2, 4)**:
- Factors of 2: 1, 2
- Factors of 4: 1, 2, 4
- Common factor: 2 (not co-prime)
9. **Pair (2, 10)**:
- Factors of 2: 1, 2
- Factors of 10: 1, 2, 5, 10
- Common factor: 2 (not co-prime)
10. **Pair (2, 12)**:
- Factors of 2: 1, 2
- Factors of 12: 1, 2, 3, 4, 6, 12
- Common factor: 2 (not co-prime)
11. **Pair (2, 22)**:
- Factors of 2: 1, 2
- Factors of 22: 1, 2, 11, 22
- Common factor: 2 (not co-prime)
12. **Pair (10, 4)**:
- Factors of 10: 1, 2, 5, 10
- Factors of 4: 1, 2, 4
- Common factor: 2 (not co-prime)
### Summary of Pairs Found
The pairs that are not co-prime are:
1. (4, 10)
2. (4, 12)
3. (4, 22)
4. (9, 15)
5. (10, 12)
6. (10, 22)
7. (12, 22)
8. (2, 4)
9. (2, 10)
10. (2, 12)
11. (2, 22)
12. (10, 4)
### Final Answer
The 12 pairs that are not co-prime are:
1. (4, 10)
2. (4, 12)
3. (4, 22)
4. (9, 15)
5. (10, 12)
6. (10, 22)
7. (12, 22)
8. (2, 4)
9. (2, 10)
10. (2, 12)
11. (2, 22)
12. (10, 4)
