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Co-prime Number

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.




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