65,535
65,535 is the highest possible port number, and the largest unsigned 16-bit integer.
- Odd
- Composite
Where 65,535 fits
Why 65,535 is special
65,535 is 2¹⁶ − 1: the ceiling of every 16-bit field, and therefore the last port a TCP or UDP connection can use. The same limit caps the maximum size of an IP packet and of a VLAN identifier's range, which is why the number turns up repeatedly in networking without ever being chosen.
Factors & digit properties
- Divisors (16)
- 1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535
- Prime factorisation
- 3 × 5 × 17 × 257
- Digit sum
- 24
- Digital root
- 6
Representations
- Decimal
- 65535
- Scientific notation
- 6.554 × 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
1 × 32,768 + 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 = 65,535
Octal
1 7 7 7 7 7
1 × 32,768 + 7 × 4,096 + 7 × 512 + 7 × 64 + 7 × 8 + 7 × 1 = 65,535
Hexadecimal
f f f f
f × 4,096 + f × 256 + f × 16 + f × 1 = 65,535
Read as powers of two: 32,768 + 16,384 + 8,192 + 4,096 + 2,048 + 1,024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 65,535.
In historical numeral systems
Egyptian
6 fingers, 5 lotuses, 5 coils of rope, 3 hobbles, 5 strokes
6 × 10,000 + 5 × 1,000 + 5 × 100 + 3 × 10 + 5 × 1 = 65,535. 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
Related numbers & connections
65,535 is 2¹⁶ − 1 and therefore the largest value a sixteen-bit field can hold — the highest TCP port, the largest IP packet, the top of a VLAN range.
View 65536 →Other connections
- is associated with65536
why?
Strength 0.50, confidence "high".
Technology & computing
65,535 is 2¹⁶ − 1, so it caps anything stored in sixteen bits: the highest TCP or UDP port, the maximum size of an IP packet, the top of a VLAN range. None of these limits was chosen — they all follow from the same field width, which is why the number recurs without ever being decided.
DocumentedTechnology & computing
Common questions
Is 65,535 a prime number?
No, 65,535 is not prime.
What are the factors of 65,535?
The factors of 65,535 are 1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535.
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