1728 (number)
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).
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← 0 [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] [[{{#expr:{{{1}}}*{{{factor}}}*1000}} (number)|{{#ifeq:{{{1}}}|10|→|{{#expr:{{{1}}}*{{{factor}}}}}k}}]] | ||||
| 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 | |||
| Octal | 33008 | |||
| Duodecimal | 100012 | |||
| Hexadecimal | 6C016 | |||
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. 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)
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