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Math K-Plus

Relative Prime Also Known As Co-Prime

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What Is A Relative Prime Also Known As A Co-Prime


If two numbers have no common factors i.e. there Greatest Common Factor is one, they are called Relative Primes; In other words, both numbers cannot evenly divide both by the same common value. For example the numbers 40 and 21 are called Relative Prime even those they are Composite Numbers. Below is an example:


As you can see the prime factors of 40 and 21 follow:
  • 40 = 1 x 2 x 2 x 2 x 5 = 4 x 10 = 8 x 5 -> factors are 1, 2, 4, 5, 8, 40
  • 21 = 1 x 3 x 7 -> factors are 1, 3, 7, and 21
There is no common divisor other than one or the number itself. That means 21 and 40 Relative-Prime also known as Co-Primes.



As you can see the prime factors of 21 and 24 follow:
  • 21 = 1 x 3 x 7 -> factors are 1, 3, 7, and 21
  • 24 = 1 x 2 x 3 x 4 = 3 x 8 = 4 x 6 -> factors are 1, 2, 3, 4, 6, 8, and 24
The numbers 1 and 3 are common factors. That means 21 and 40 are NOT relative-primes and NOT co-primes.