what is mean by coprime
Answers
Two integers are said to be coprimes or relatively prime to each other, if the two have no common factors except 1.
In other words, if the HCF (Highest Common Factor) of two numbers is 1, then the numbers are called coprime integers, or simply, coprimes.
Or we say that one among the two integers is relatively prime to the other.
Pairs of such coprime integers are given below:
(2, 3), (3, 5), (2, 7), (9, 17), (13, 23), (31, 57), (49, 50), (91, 97)
Algebraically, we say two integers a and b are coprimes if HCF(a, b) = 1.
And also it is always true that, any two consecutive integers are coprimes.
(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (9, 10)... are pairs having coprime integers.
If we consider an integer, let 'n', there may be a definite number of integers strictly less than or equal to 'n' which are relatively prime to 'n'. The no. of such integers is called the totient function of 'n'. This function is denoted by φ(n). [φ - Greek letter 'phi']
E.g.: φ(5) = 4 because the integers 1, 2, 3, 4 each, which are less than 5, are relatively prime to 5.
φ(1) = 1 since HCF(1, 1) = 1.
And also, for every prime number p, φ(p) = p - 1.
Answer:
Of two or more numbers in relation to each other: having no common integral factor except unity.
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