To determine which statement is true for the numbers 56 and 84, we will analyze the options provided.
### Step-by-Step Solution:
1. **Identify if 56 and 84 are prime numbers:**
- A prime number has only two factors: 1 and itself.
- 56 has factors: 1, 2, 4, 7, 8, 14, 28, 56 (not prime).
- 84 has factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 (not prime).
- **Conclusion:** Neither 56 nor 84 is a prime number.
**Hint:** Check the definition of prime numbers and list the factors of each number.
2. **Check if 56 and 84 are co-prime:**
- Co-prime numbers have no common factors other than 1.
- The common factors of 56 and 84 are: 1, 2, 4, 7, 14, 28.
- **Conclusion:** They are not co-prime since they have common factors other than 1.
**Hint:** List the factors of both numbers and identify any common factors.
3. **Determine if both are factors of 14:**
- Factors of 14 are: 1, 2, 7, 14.
- 56 is not a factor of 14.
- 84 is not a factor of 14.
- **Conclusion:** Neither 56 nor 84 is a factor of 14.
**Hint:** List the factors of 14 and check if 56 and 84 are included.
4. **Check if both are odd numbers:**
- Odd numbers are not divisible by 2.
- 56 is even (divisible by 2).
- 84 is even (divisible by 2).
- **Conclusion:** Neither 56 nor 84 is an odd number.
**Hint:** Check the divisibility of each number by 2.
5. **Final Conclusion:**
- Since none of the options are true, we conclude that none of the statements provided (both are prime numbers, both are co-prime, both are factors of 14, both are odd numbers) are correct.
### Summary of Findings:
- 56 and 84 are not prime numbers.
- They are not co-prime.
- They are not factors of 14.
- They are not odd numbers.
**Final Answer:** None of the statements are true for 56 and 84.
