Co prime and twin prime

Concepts: Twin Prime & Co-Prime Numbers

Twin Prime Numbers:

Twin prime numbers are pairs of prime numbers that differ by exactly 2. For example:

• (3, 5)
• (5, 7)
• (11, 13)
• (17, 19)
• (29, 31)

Co-Prime Numbers:

Co-prime numbers are pairs of natural numbers whose highest common factor (HCF) is 1. They do not share any other common factor except 1. For example:

• (4, 9) – HCF = 1
• (7, 10) – HCF = 1
• (8, 15) – HCF = 1

Note: Co-prime numbers need not both be prime.

Quiz: Twin Prime & Co-Prime Numbers

1. Which of the following is a pair of twin prime numbers?

A) 11 and 14 B) 11 and 13 C) 13 and 17 D) 17 and 21

2. The pair (7, 10) is an example of:

A) Twin primes B) Even numbers C) Co-prime numbers D) Composite numbers

3. Which of the following pairs is NOT a twin prime pair?

A) (5, 7) B) (17, 19) C) (29, 31) D) (23, 29)

4. Which of the following is true for co-prime numbers?

A) Their difference is 2 B) They are always prime C) Their HCF is always 1 D) They are always even

5. What is the HCF of 8 and 15?

A) 2 B) 1 C) 3 D) 5

6. Which of the following pairs are both prime but not twin primes?

A) 11 and 13 B) 17 and 19 C) 13 and 17 D) 3 and 5

7. The pair (25, 28) is:

A) Prime B) Co-prime C) Twin prime D) Neither prime nor co-prime

8. Which of the following statements is incorrect?

A) All prime numbers are co-prime B) All co-prime numbers are natural numbers C) Co-prime numbers must have HCF as 1 D) Two even numbers can be co-prime

9. Which is the smallest pair of twin prime numbers?

A) (3, 5) B) (2, 3) C) (5, 7) D) (7, 11)

10. Are 15 and 28 co-prime?

A) Yes, because both are odd B) No, because both are composite C) Yes, because their HCF is 1 D) No, because their LCM is not a multiple of either