In mathematics, two integers (a and b) are co-prime (or relatively prime) if they share no common factors. In other words, there is no number, other than 1, that divides both a and b evenly. The highest common factor (HCF) of these numbers should be 1
As an example, 6 and 35 are coprime, because the factors of 6, 2 and 3, do not divide 35 evenly. 6 and 27 are not coprime, because 3 divides both 6 and 27. Another example is 4 and 5: 4 = 2*2*1; 5 = 5*1 (Prime). The only common factor is 1, so they are co-prime.
Likewise 10 and 5: 10 = 5*2
5 = 5*1 (Prime). The common factors are 5 and 1 so they are not co-prime.
Properties of Co-prime[change | change source]
- Prime numbers are always co-prime to each other.
- Any two consecutive integers are always co-prime.
- Sum of any two coprime numbers is always coprime to their product.
- 1 is trivially coprime with all numbers.
- if out of two numbers, any one number is a prime number while other number is not a multiple of first one, then both are coprime.
- This is not applicable to negative numbers
If the HCF of 2 numbers is 1 then they are co prime.