gcd18

gcd18 is a term used in mathematics and computer science to denote the greatest common divisor of the fixed integer 18 with another integer. Formally, gcd18(n) = gcd(18, n). Since 18 factors as 2 times 3 squared, the gcd must be one of the positive divisors of 18: 1, 2, 3, 6, 9, or 18.

For example, gcd18(24) equals 6, since 18 and 24 share the divisors 1, 2, 3, and 6, with 6 being the largest. gcd18(35) equals 1, because 35 shares no common prime factors with 18 other than 1. Other quick examples include gcd18(9) = 9 and gcd18(18) = 18. Negative inputs do not affect the result, as gcd is defined for the absolute value of the numbers involved.

Computation of gcd18 can be done with the Euclidean algorithm, but because one argument is fixed at 18, a practical approach is to check divisibility by the divisors of 18 and select the largest divisor that divides the second input. This reduces the problem to a small set of checks when dealing with typical integer sizes.

Properties of gcd18 include that all possible outputs are divisors of 18, and the value reflects the overlap of prime factors between 18 and the other integer. The concept serves as a simple, concrete example for explaining the greatest common divisor, factorization, and modular arithmetic, and it is often used in teaching, examples in algorithms, and small-scale numerical applications.