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).

← 1727 1728 1729 →
List of numbers — Integers ← 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	2^6 × 3^3
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)