divisibleby18

Divisibleby18 refers to the divisibility property of integers by the number 18. An integer n is divisible by 18 if there exists an integer k such that n = 18k.

Because 18 equals 2 times 3 squared, divisibility by 18 is equivalent to being divisible by both 2 and 9. In decimal form this means the number is even (its last digit is 0, 2, 4, 6, or 8) and the sum of its digits is a multiple of 9. Since 2 and 9 are coprime, these two conditions together guarantee divisibility by 18.

The set of integers divisible by 18 is the set of all multiples of 18: {..., -36, -18, 0, 18, 36, 54, ...}. This forms an infinite arithmetic progression with common difference 18. If a number is divisible by 18, then n/18 is an integer.

In modular arithmetic, a number is divisible by 18 precisely when it is congruent to 0 modulo 18, i.e., n ≡ 0 (mod 18). This concept is often used in problems involving common multiples or modular constraints, and in programming it can be checked with a test such as n % 18 == 0.

Examples of positive multiples include 18, 36, 54, 72, 90, and 108; corresponding negative multiples are -18, -36, etc.