A set of numbers which do not have any other common factor other than 1 are called co-prime or relatively prime numbers. This means those numbers whose HCF is 1.

Don't confuse co prime number with Prime number although its true all prime numbers are coprime to each other but non-prime number can be coprime to each other too.

Example :- 8 and 9
8 = 2 * 2 * 2
9 = 3 * 3
so 8 and 9, they dont have any common factor other than 1 so 8 and 9 are coprime to each other.

Properties Of Co-prime Numbers:

1 - All prime numbers are co-prime to each other.
Ex. 11 and 29

2 - Any 2 consecutive integers are always co-prime.
Ex. 11 and 13

3 - Sum of any two co-prime numbers is always co-prime with their product.
Ex. 8 and 9,
8+9(17) will be co-prime to 8*9(72)

4 - 1 is co-prime with all numbers.

5 - a and b (natural numbers) are co-prime only if the numbers 2a-1 and 2b-1 are co-prime.
Ex. 8 and 9,
(2*8-1) = 15 and (2*9)-1 = 17 are co-prime to each other.