multipleoffour

Multipleoffour refers to the set of integers that are divisible by four. In number theory this set is commonly denoted 4Z or {4n : n ∈ Z}. Elements have the form 4n, where n is any integer, so the sequence includes 0, 4, 8, 12, 16, and also negative multiples such as -4 and -8. The collection forms an infinite arithmetic progression with common difference 4 and is closed under addition and subtraction; the sum or difference of two multiples of four is again a multiple of four. An integer a belongs to multipleoffour exactly when a mod 4 = 0.

A standard divisibility criterion is that a number is divisible by 4 if its last two decimal digits form a number divisible by 4. In binary terms, a number is divisible by 4 if its last two binary digits are zero.

Counting and density: among any block of N consecutive integers, about N/4 are multiples of four. Consequently, the asymptotic density of the set 4Z within the integers is 1/4.

Examples of multiples of four include 0, 4, 8, 12, 16, and their negative counterparts. Applications appear in areas such as computer memory alignment, where data structures are often organized on 4-unit boundaries, and in algorithms that iterate in steps of four. Related concepts include multiples of other integers and arithmetic progressions, as well as modular arithmetic with modulus 4.