gcd14

Gcd14 is a term that can be used in mathematics to denote the greatest common divisor of 14 and another integer. More formally, gcd14(n) can be read as gcd(14, n), the largest positive integer that divides both 14 and n.

Because 14 factors as 2 × 7, the gcd of 14 with any integer n is always one of the divisors of 14: 1, 2, 7, or 14. It equals 1 if n is coprime to 14 (not divisible by 2 or 7), equals 2 if n is even but not divisible by 7, equals 7 if n is divisible by 7 but not by 2, and equals 14 if n is divisible by both 2 and 7. For example, gcd14(1) = 1, gcd14(10) = 2, gcd14(21) = 7, and gcd14(28) = 14.

Computationally, gcd(14, n) can be obtained via the Euclidean algorithm or by reducing n modulo 14, since gcd(14, n) = gcd(14, n mod 14). This makes the calculation straightforward even for large n, because the modulo operation confines the problem to a small range.

In other contexts, gcd14 may be used as a code name, identifier, or version tag in software, documentation, or organizational systems. As a mathematical term, however, its primary meaning remains the greatest common divisor of 14 and another integer.