56 (number) — properties, representations, and notable facts

Overview of the integer 56: its mathematical properties, divisors and factorization, numeric representations, combinatorial appearances, and occurrences in science and everyday uses.

Overview

56 is a whole number that lies between fifty-five and fifty-seven. It is an even number, a composite integer with multiple divisors and several commonplace appearances in mathematics and the applied sciences. As a positive integer it is studied for its algebraic structure, combinatorial roles, and simple numerical representations.

Mathematical properties

Its prime factorization is 2³ × 7, which shows 56 is divisible by smaller integers. It has eight positive divisors and is classified as an abundant number because the sum of its proper divisors exceeds the number itself. You can check basic divisibility facts such as it being divisible by 1 as well as by 2, 4, 7, 8, 14, and 28.

Divisors: 1, 2, 4, 7, 8, 14, 28, 56
Prime factorization: 2³ × 7
Classification: even, composite, abundant

Special numeric forms and combinatorics

56 is notable for several structural roles: it is a pronic number (the product of two consecutive integers, 7 × 8), and a tetrahedral (or triangular pyramidal) number, meaning it can be arranged as a three-dimensional pyramid with a triangular base. In combinatorics it appears as a binomial coefficient: for example, C(8,3) = 56, so it counts certain combinations of 8 items taken 3 at a time.

Representations and notations

Common numeric representations include binary 111000, hexadecimal 38, and Roman numerals LVI. Its digit sum in base ten is 11. These compact notations make 56 easy to identify across different numbering systems and in computational contexts.

Occurrences and uses

Beyond pure mathematics, 56 appears in science and practical lists: it is the atomic number of the element barium, and in telecommunications +56 is the international dialing code for Chile. Its arithmetic properties make it useful as a product and factor in problems that involve grouping, tiling, or discrete counts where 7 and 8 play a role.

Notable facts and distinctions

Because 56 combines a power of two with a distinct odd prime factor it often arises in elementary number-theory examples and classroom exercises. Its presence in Pascal's triangle and as a tetrahedral number links two different branches of combinatorial and geometric thinking, offering multiple ways to visualize the same integer.