32,767
32,767 is 2¹⁵ − 1: the largest value a signed 16-bit integer can hold.
- Odd
- Composite
Why 32,767 is special
It is the ceiling that 8-bit and 16-bit systems ran into constantly, and it survives in file formats and protocol fields designed when 16 bits was a sensible width. Anything counting past it in a signed 16-bit field wraps to −32,768, which is why old games cap scores and inventories at oddly specific numbers.
Factors & digit properties
- Divisors (8)
- 1, 7, 31, 151, 217, 1057, 4681, 32767
- Prime factorisation
- 7 × 31 × 151
- Digit sum
- 25
- Digital root
- 7
Representations
- Decimal
- 32767
- Scientific notation
- 3.277 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 × 16,384 + 1 × 8,192 + 1 × 4,096 + 1 × 2,048 + 1 × 1,024 + 1 × 512 + 1 × 256 + 1 × 128 + 1 × 64 + 1 × 32 + 1 × 16 + 1 × 8 + 1 × 4 + 1 × 2 + 1 × 1 = 32,767
Octal
7 7 7 7 7
7 × 4,096 + 7 × 512 + 7 × 64 + 7 × 8 + 7 × 1 = 32,767
Hexadecimal
7 f f f
7 × 4,096 + f × 256 + f × 16 + f × 1 = 32,767
Read as powers of two: 16,384 + 8,192 + 4,096 + 2,048 + 1,024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 32,767.
In historical numeral systems
Egyptian
3 fingers, 2 lotuses, 7 coils of rope, 6 hobbles, 7 strokes
3 × 10,000 + 2 × 1,000 + 7 × 100 + 6 × 10 + 7 × 1 = 32,767. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
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
- Deficient number
Technology & computing
The largest value a signed 16-bit integer can hold is 32,767 (worldwide, two's complement). Anything counting past it in a signed 16-bit field wraps to −32,768, which is why older software caps scores and inventories at oddly specific numbers.
DocumentedTechnology & computingGeography: worldwide, two's complement
Common questions
Is 32,767 a prime number?
No, 32,767 is not prime.
What are the factors of 32,767?
The factors of 32,767 are 1, 7, 31, 151, 217, 1057, 4681, 32767.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 15 July 2026