1,728
1,728 is a great gross — 12³ — and the number of cubic inches in a cubic foot.
Where 1,728 fits
Why 1,728 is special
1,728 is what happens when a duodecimal habit meets three dimensions. Twelve inches to a foot means 12 × 12 × 12 cubic inches to a cubic foot, and the same cube gives the 'great gross' of the old counting system: twelve dozen dozen. It is why imperial volume conversions carry such awkward numbers.
Same number, different meanings
How 1,728 is understood across different contexts — never implying one meaning because of another.
- Mathematics
1,728 is what happens when a duodecimal habit meets three dimensions. Twelve inches to a foot means 12 × 12 × 12 cubic inches to a cubic foot, and the same cube gives the 'great gross' of the old counting system: twelve dozen dozen. It is why imperial volume conversions carry such awkward numbers.
- History
In 1728, Vitus Bering sailed the strait between Asia and North America, establishing that the continents are separate (North Pacific).
- Everyday life
Twelve inches to a foot cubes to 1,728 cubic inches in a cubic foot. The same number is a great gross — twelve dozen dozen — from an older counting system built on twelves. Metric volume conversions are powers of ten precisely to avoid arriving at numbers like this.
1,728 is part of
Factors & digit properties
- Divisors (28)
- 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
- Prime factorisation
- 2^6 × 3^3
- Digit sum
- 18
- Digital root
- 9
Representations
- Decimal
- 1728
- Scientific notation
- 1.728 × 10^3
Roman numerals
M D C C X X V I I I
Binary
1 1 0 1 1 0 0 0 0 0 0
1 × 1,024 + 1 × 512 + 0 × 256 + 1 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 1,728
Octal
3 3 0 0
3 × 512 + 3 × 64 + 0 × 8 + 0 × 1 = 1,728
Hexadecimal
6 c 0
6 × 256 + c × 16 + 0 × 1 = 1,728
Read as powers of two: 1,024 + 512 + 128 + 64 = 1,728.
In historical numeral systems
Egyptian
1 lotus, 7 coils of rope, 2 hobbles, 8 strokes
1 × 1,000 + 7 × 100 + 2 × 10 + 8 × 1 = 1,728. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
2 corner wedges + 8 vertical wedges (sixties place), 4 corner wedges + 8 vertical wedges (units place)
28 × 60 + 48 = 1728. Places are separated by a space on the tablet, with the higher place written first.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Abundant number
- Powerful number
- Harshad (Niven) number
Related numbers & connections
1,728 is twelve gross, or twelve cubed: the number of cubic inches in a cubic foot. Both numbers come from the same habit of counting in twelves.
View 144 →1728 is a year in the 18th century, in the 1720s.
Twelve inches to a foot cubes to 1,728, which is why imperial volume conversions produce numbers no one can do in their head.
View 12 →History
In 1728, Vitus Bering sailed the strait between Asia and North America, establishing that the continents are separate (North Pacific).
DocumentedHistoryGeography: North PacificPeriod: 1728
Everyday life
Twelve inches to a foot cubes to 1,728 cubic inches in a cubic foot. The same number is a great gross — twelve dozen dozen — from an older counting system built on twelves. Metric volume conversions are powers of ten precisely to avoid arriving at numbers like this.
DocumentedEveryday life
Common questions
Is 1,728 a prime number?
No, 1,728 is not prime.
What are the factors of 1,728?
The factors of 1,728 are 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.
What is 1,728 in Roman numerals?
1,728 in Roman numerals is MDCCXXVIII.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 2 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026