WHAT ARE CO-PRIME NUMBER`S?
Answers
the number which have 1 as common factor ie co prime numbers
Answer:
In number theory, two integers a and b are said to be relatively prime, mutually prime,[1] or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1. Consequently, any prime number that divides one does not divide the other. This is equivalent to their greatest common divisor (gcd) being 1.
The numerator and denominator of a reduced fraction are co prime. As specific examples, 14 and 15 are co prime, being commonly divisible only by 1, while 14 and 21 are not coprime, because they are both divisible by 7.
Standard notations for relatively prime integers a and b are: gcd(a, b) = 1 and (a, b) = 1. Graham, Knuth and Patashnik have proposed that the notation {\displaystyle a\perp b}a\perp b be used to indicate that a and b are relatively prime and that the term "prime" be used instead of coprime (as in a is prime to b).
A fast way to determine whether two numbers are coprime is given by the Euclidean algorithm and its faster variants such as binary GCD algorithm or Lehmer's GCD algorithm.
The number of integers coprime to a positive integer n, between 1 and n, is given by Euler's totient function (or Euler's phi function) φ(n).
A set of integers can also be called coprime if its elements share no common positive factor except 1. A stronger condition on a set of integers is pairwise coprime, which means that a and b are coprime for every pair (a, b) of different integers in the set. The set {2, 3, 4} is coprime, but it is not pairwise coprime since 2 and 4 are not relatively prime.
Step-by-step explanation:
For example, 2 and 3 are two prime numbers. Factors of 2 are 1, 2 and factors of 3 are 1, 3. The only common factor is 1 and hence is co-prime. Any two successive numbers/ integers are always co-prime: Take any consecutive number such as 2, 3 or 3, 4 or 5, 6 and so on; they have 1 as their HCF.
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