# 1728 (number)

 ← 1727 1728 1729 →
Cardinal one thousand seven hundred twenty-eight
Ordinal 1728th
(one thousand seven hundred twenty-eighth)
Factorization 26× 33
Greek numeral ,ΑΨΚΗ´
Roman numeral MDCCXXVIII
Binary 110110000002
Ternary 21010003
Quaternary 1230004
Quinary 234035
Senary 120006
Octal 33008
Duodecimal 100012
Vigesimal 46820
Base 36 1C036

1728 is the natural number following 1727 and preceding 1729. 1728 is a dozen gross, one great gross (or grand gross, or, in Germanic, Mass[citation needed]).

## In mathematics

1728 is the cube of 12 and, as such, is important in the duodecimal number system, in which it is represented as "1000". It is the number of cubic inches in a cubic foot. 1728 occurs in the algebraic formula for the j-invariant of an elliptic curve. As a consequence, it is sometimes called a Zagier as a pun on the Gross–Zagier theorem.[citation needed] The number 1728 is one less than the Ramanujan number 1729.

• 1728 = 123
• 1728 = 33 × 43
• 1728 = 23 × 63
• 1728 = 63 + 83 + 103
• 1728 = 242 + 242 + 242
• 1728 = 2893 + 2873 + (-288)3 + (-288)3
• Divisors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728

1728 is also the number of directed open knight's tours on a 5 × 5 chessboard. (sequence A165134 in the OEIS)