Coprime

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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 HCF [1] 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 factors are 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]

1. Prime numbers are always co-prime to each other.

2. Any two consecutive integers are always co-prime.

3. Sum of any two coprime numbers is always coprime to their product.

4. 1 is trivially coprime with all numbers.

5. 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.

6. This is not applicable to negative numbers

If the HCF of 2 numbers is 1 then they are co prime.

  1. "HCF". https://en.wikipedia.org/wiki/Greatest_common_divisor.