1728 (number)

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← 1727 1728 1729 →
Cardinalone thousand seven hundred twenty-eight
Ordinal1728th
(one thousand seven hundred twenty-eighth)
Factorization26 × 33
Greek numeral,ΑΨΚΗ´
Roman numeralMDCCXXVIII
Binary110110000002
Ternary21010003
Octal33008
Duodecimal100012
Hexadecimal6C016

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[edit]

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 Hardy–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).

1728 is also the number of daily chants of the Hare Krishna (mantra) by a Hare Krishna devotee. The number comes from 16 rounds on a 108 japamala bead.