This is the latest accepted revision, reviewed on 9 January 2023. Jump to navigation Jump to search This article is about the number. For the 4th of july bbq ideas, see AD 4. It is the natural number following 3 and preceding 5.

Four is the smallest composite number, its proper divisors being 1 and 2. By consequence, four is the only square one more than a prime number, specifically three. Each natural number divisible by 4 is a difference of squares of two natural numbers, i. A number is a multiple of 4 if its last two digits are a multiple of 4. Lagrange’s four-square theorem states that every positive integer can be written as the sum of at most four square numbers. There are four all-Harshad numbers: 1, 2, 4, and 6.

12, which is divisible by four thrice over, is a Harshad number in all bases except octal. A four-sided plane figure is a quadrilateral or quadrangle, sometimes also called a tetragon. It can be further classified as a rectangle or oblong, kite, rhombus, and square. Four is the highest degree general polynomial equation for which there is a solution in radicals.

A solid figure with four faces as well as four vertices is a tetrahedron, which is the smallest possible number of faces and vertices a polyhedron can have. 5-cell, 8-cell or tesseract, 16-cell, 24-cell, 120-cell, and 600-cell. Two-dimensional: infinitely many regular star polygons. Three-dimensional: four regular star polyhedra, the regular Kepler-Poinsot star polyhedra.

Four-dimensional differential manifolds have some unique properties. The quaternions loose a further commutative algebraic property, while holding associative, alternative, and power-associative properties. The octonions are alternative and power-associative, while the sedenions are only power-associative. 2, 4, 8, and 16, respectively. Brahmic numerals represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign.