Which of the following pairs of numbers are NOT co-primes? a. 16 and 25 b. 26 and 35 c. 36 and 45 d. 46 and 55

To determine which pairs of numbers are **not co-primes**, we need to check if their greatest common divisor (GCD) is greater than 1. If two numbers have a GCD of 1, they are co-primes; otherwise, they are not.

Let's check each pair:

- **(a) 16 and 25**  
  Factors of 16: \( 1, 2, 4, 8, 16 \)  
  Factors of 25: \( 1, 5, 25 \)  
  Common factor: \( 1 \)  
  Since the GCD is 1, **16 and 25 are co-primes**.

- **(b) 26 and 35**  
  Factors of 26: \( 1, 2, 13, 26 \)  
  Factors of 35: \( 1, 5, 7, 35 \)  
  Common factor: \( 1 \)  
  Since the GCD is 1, **26 and 35 are co-primes**.

- **(c) 36 and 45**  
  Factors of 36: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)  
  Factors of 45: \( 1, 3, 5, 9, 15, 45 \)  
  Common factors: \( 1, 3, 9 \)  
  Since the GCD is 9 (greater than 1), **36 and 45 are not co-primes**.

- **(d) 46 and 55**  
  Factors of 46: \( 1, 2, 23, 46 \)  
  Factors of 55: \( 1, 5, 11, 55 \)  
  Common factor: \( 1 \)  
  Since the GCD is 1, **46 and 55 are co-primes**.

### Conclusion:
The pair **36 and 45** are **not co-primes**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How can you find the GCD of two numbers quickly?
2. What are some efficient methods for determining if two numbers are co-prime?
3. Can two even numbers ever be co-prime? Why or why not?
4. Are consecutive numbers always co-prime?
5. How does the prime factorization of two numbers relate to their co-primality?

**Tip:** If two numbers have no common prime factors, they are co-prime.

Determine which pair of numbers is not co-prime by calculating the greatest common divisor (GCD). This problem covers essential number theory concepts like co-primes and GCD. Ideal for students in Grades 6-8.

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