What are relatively prime numbers?
short answers for big questions
The answer to this question is quite simple. Two numbers are called prime between each other when their own common divisor corresponds to the unit. Thus we have that the greatest common divisor (GCD) between those two numbers is number 1.
Sorry but I didn’t understand. Could you give an example?
Of course, I could. So, the divisors of number 4 are the following ones: `{1,2,4}`; the divisors of number 9 are these ones: `{1,3,9}`. The only common divisor between 4 and 9 is number 1, so 4 and 9 are "prime with respect to each other". Regarding the number 15 and 21, they are not relatively primes, since besides number 1 they also have number 3 as a common divisor.
Can I arrive to the conclusion that numbers don’t even need to be prime?
Actually, they don’t need it. For instance, numbers 25 and 27 are relatively prime numbers; however none of them are prime itself.
And if both of them are prime?
Two prime numbers are always relatively prime numbers. According to the definition of a prime number we can notice that these numbers only have two divisors, which are themselves and the unit. Thus, the only common divisor between two prime numbers is the unit for sure. By the way, so as to take a conclusion, it is useful for you to know that two consecutive numbers are always prime between each other. To explain this fact is a little more complex, but for the most curious ones let’s say that if two consecutive numbers had a common divisor different from the unit, this divisor would have to be divisor of the difference between both numbers. However, as the difference between two consecutive numbers equals one, that common divisor would be divisor of number one, which is impossible!
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