Cardinal Cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...	One thousand, seven hundred [and] twenty-eight
Ordinal Ordinal number In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...	1728th
Factorization Factorization In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original...
Roman numeral	MDCCXXVIII
Binary Binary numeral system The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...	11011000000
Octal Octal The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...	3300
Duodecimal Duodecimal The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...	1000
Hexadecimal Hexadecimal In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...	6C0

1728 is the natural number

Natural number

In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

 following 1727 and preceding 1729

1729 (number)

1729 is the natural number following 1728 and preceding 1730.1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Ramanujan...

. 1728 is a dozen

Dozen

A dozen is a grouping of approximately twelve. The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the moon or months in a cycle of the sun or year...

 gross

Gross (unit)

A gross is equal to a dozen dozen, i.e. 12 × 12 = 144.It can be used in duodecimal counting. The use of gross likely originated from the fact that 144 can be counted on the fingers using the fingertips and first two joints of each finger when marked by the thumb of one hand. The other hand...

, one great gross (or grand gross, or, in Germanic, Mass).

In mathematics

It is the cube

Cube (arithmetic)

In arithmetic and algebra, the cube of a number n is its third power — the result of the number multiplying by itself three times:...

 of 12

12 (number)

12 is the natural number following 11 and preceding 13.The word "twelve" is the largest number with a single-morpheme name in English. Etymology suggests that "twelve" arises from the Germanic compound twalif "two-leftover", so a literal translation would yield "two remaining [after having ten...

 and, as such, is important in the duodecimal

Duodecimal

The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...

 number system. It is the number of cubic inches in a cubic foot. 1728 occurs in the algebraic formula for the j-invariant

J-invariant

In mathematics, Klein's j-invariant, regarded as a function of a complex variable τ, is a modular function defined on the upper half-plane of complex numbers.We haveThe modular discriminant \Delta is defined as \Delta=g_2^3-27g_3^2...

 of an elliptic curve

Elliptic curve

In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...

. As a consequence, it is sometimes called a Zagier as a pun on the Gross–Zagier theorem.

• 1728 = 12³
• 1728 = 3³ × 4³
• 1728 = 2³ × 6³
• 1728 = 6³ + 8³ + 10³
• 1728 = 24² + 24² + 24²

17 = 2 + 3 + 5 + 7         (The sum of the first four prime numbers)

28 = 2 + 3 + 5 + 7 + 11 (The sum of the first five prime numbers)