Q 20 - Which of the following is a pair of Co-primes?

A - (14, 35)

B - (18, 25)

C - (31, 93)

D - (32,62)'

To determine which of the given pairs are co-primes, we need to find a pair of numbers that have no common factors other than 1. In other words, the greatest common divisor (GCD) of the two numbers must be 1.

Let's evaluate each pair:

- **A - (14, 35):**
  - Factors of 14: 1, 2, 7, 14
  - Factors of 35: 1, 5, 7, 35
  - Common factors: 1, 7
  - Since 7 is a common factor, this pair is **not** co-prime.

- **B - (18, 25):**
  - Factors of 18: 1, 2, 3, 6, 9, 18
  - Factors of 25: 1, 5, 25
  - Common factor: 1
  - Since the only common factor is 1, this pair **is** co-prime.

- **C - (31, 93):**
  - Factors of 31: 1, 31 (31 is a prime number)
  - Factors of 93: 1, 3, 31, 93
  - Common factor: 1, 31
  - Since 31 is a common factor, this pair is **not** co-prime.

- **D - (32, 62):**
  - Factors of 32: 1, 2, 4, 8, 16, 32
  - Factors of 62: 1, 2, 31, 62
  - Common factor: 1, 2
  - Since 2 is a common factor, this pair is **not** co-prime.

**Answer: B - (18, 25)** is the pair of co-primes.

Would you like further details or have any questions?

### Related Questions:
1. What is the definition of a co-prime pair?
2. How do you find the GCD of two numbers?
3. Can a prime number and a composite number ever be co-primes?
4. What is the significance of co-prime numbers in number theory?
5. How would you determine if a pair like (9, 28) is co-prime?

**Tip:** Always check the factors of both numbers in a pair to determine if they are co-prime.

Q 20 - Which of the following is a pair of Co-primes? A - (14, 35) B - (18, 25) C - (31, 93) D - (32, 62)

Explore how to identify co-prime numbers with this example question: Which of the following is a pair of co-primes? (14, 35), (18, 25), (31, 93), or (32, 62). Learn the process of finding the greatest common divisor (GCD) and determining co-prime pairs in number theory. Suitable for Grades 6-8.

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