Find out which of the following sets form **co-prime numbers**:

(a) (12, 7)

(b) (21, 42)

(c) (43, 129)

(d) (3, 9)

Question

Find out which of the following sets form **co-prime numbers**:

(a) (12, 7)

(b) (21, 42)

(c) (43, 129)

(d) (3, 9)

Accepted Answer

**Solution:**

1. Two numbers are **co-prime** if their Highest Common Factor (HCF) is 1.

2. Calculate HCF of each pair:

- (12, 7):
     - Factors of 12: 1, 2, 3, 4, 6, 12
     - Factors of 7: 1, 7
     - Common factors: 1
     - HCF = 1 → Co-prime

- (21, 42):
     - Factors of 21: 1, 3, 7, 21
     - Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
     - Common factors: 1, 3, 7, 21
     - HCF = 21 → Not co-prime

- (43, 129):
     - 43 is a prime number.
     - Check if 43 divides 129:
       - 129 ÷ 43 = 3 (exact)
     - So, HCF = 43 → Not co-prime

- (3, 9):
     - Factors of 3: 1, 3
     - Factors of 9: 1, 3, 9
     - Common factors: 1, 3
     - HCF = 3 → Not co-prime

**Correction:** On rechecking (43, 129), since 43 divides 129 exactly, their HCF is 43, so they are **not** co-prime.

**Final check:**
- Only (12, 7) have HCF = 1.

**Answer:** Only the set (12, 7) forms co-prime numbers.

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