**What is a Co-prime number?**

Two numbers are said to be co-prime numbers, if they don’t have any common factor other than 1.

**Co-prime Numbers Examples**

**Example 1**

Which of the following are co-prime numbers?

a) 9 and 12

b) 5 and 10

c) 3 and 6

**d) 2 and 5**

**Explanation**

Two numbers are said to be co-prime numbers, if they don’t have any common factor other than 1.

Here,

9 and 12

Factors of 9 are 3 x 3

Factors of 12 are 3 x 2 x 2

Since, both 9 and 12 have common factor 3 so they are not co-primes.

5 and 10 have factors other than 1

Factors of 5 are 5 x 1

Factors of 10 are 5 x 2

Since, both 5 and 10 have common factor 5 so they are not co-primes.

3 and 6

Factors of 3 are 3 x 1

Factors of 6 are 3 x 2

Since, both 3 and 6 have common factor 3 so they are not co-primes.

2 and 5

Factors of 2 are 2 x 1

Factors of 5 are 5 x 1

Since, both 2 and 5 do not have common factor other than 1. so they are co-primes.

therefore, 2 and 5 are co-prime numbers.

**Example 2**

Which of the following are co-prime numbers?

**a) 3 and 4**

b) 10 and 12

c) 4 and 6

d) 8 and 4

**Explanation**

Two numbers are said to be co-prime numbers, if they don’t have any common factor other than 1.

Here,

3 and 4

Factors of 3 are 3 x 1

Factors of 4 are 4 x 1

Since, both 3 and 4 do not have common factor other than 1. so they are co-primes.

10 and 12

Factors of 10 are 2 x 5

Factors of 12 are 2 x 2 x 3

Since, both 10 and 12 have common factor 2 so they are not co-primes.

4 and 6

Factors of 4 are 2 x 2

Factors of 6 are 2 x 3

Since, both 4 and 6 have common factor 2 so they are not co-primes.

8 and 4 have factors other than 1

Factors of 8 are 2 x 2 x 2

Factors of 4 are 2 x 2

Since, both 8 and 4 have common factor 2 and 2 x 2 = 4 so they are not co-primes.

therefore, 3 and 4 are co-prime numbers.

**Example 3**

Which of the following are co-prime numbers?

a) 12 and 14

b) 10 and 12

**c) 5 and 7**

d) 6 and 8

**Explanation**

Two numbers are said to be co-prime numbers if they don’t have a common factor other than 1.

Here,

12 and 14

Factors of 12 are 2 x 2 x 3

Factors of 14 are 2 x 7

Since, both 12 and 14 have common factor 2 so they are not co-primes.

10 and 12 have factors other than 1

Factors of 10 are 2 x 5

Factors of 12 are 2 x 2 x 3

Since, both 10 and 12 have common factor 2 so they are not co-primes.

5 and 7

Factors of 5 are 5 x 1

Factors of 7 are 7 x 1

Since, both 5 and 7 do not have common factor other than 1. so they are co-primes.

6 and 8

Factors of 6 are 2 x 3

Factors of 8 are 2 x 2 x 2

Since, both 6 and 8 have common factor 2 so they are not co-primes.

therefore, 5 and 7 are co-prime numbers.

**Example 4**

Which of the following are co-prime numbers?

a) 18 and 6

**b) 11 and 12**

c) 7 and 14

d) 16 and 8

**Explanation**

Two numbers are said to be co-prime numbers if they don’t have a common factor other than 1.

Here,

18 and 6

Factors of 18 are 2 x 3 x 3

Factors of 6 are 2 x 3

Since, both 18 and 6 have common factor 2 and 2 x 3 = 6 so they are not co-primes.

11 and 12

Factors of 11 are 11 x 1

Factors of 12 are 2 x 2 x 3

Since, both 11 and 12 do not have common factor other than 1. so they are co-primes.

7 and 14

Factors of 7 are 7 x 1

Factors of 14 are 7 x 2

Since, both 7 and 14 have common factor 7 so they are not co-primes.

16 and 8 have factors other than 1

Factors of 16 are 2 x 2 x 2 x 2

Factors of 8 are 2 x 2 x 2

Since, both 16 and 8 have common factor 2 so they are not co-primes.

therefore, 11 and 12 are co-prime numbers.