56,000
56 kbps was the practical ceiling for dial-up modems.
- Even
- Composite
Where 56,000 fits
Why 56,000 is special
The limit comes from the telephone network's own digital encoding rather than from the modem, so no amount of engineering could exceed it. Broadband required abandoning the voice channel entirely.
Factors & digit properties
- Divisors (56)
- 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 64, 70, 80, 100, 112, 125, 140, 160, 175, 200, 224, 250, 280, 320, 350, 400, 448, 500, 560, 700, 800, 875, 1000, 1120, 1400, 1600, 1750, 2000, 2240, 2800, 3500, 4000, 5600, 7000, 8000, 11200, 14000, 28000, 56000
- Prime factorisation
- 2^6 × 5^3 × 7
- Digit sum
- 11
- Digital root
- 2
Representations
- Decimal
- 56000
- Scientific notation
- 5.600 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 0
1 × 32,768 + 1 × 16,384 + 0 × 8,192 + 1 × 4,096 + 1 × 2,048 + 0 × 1,024 + 1 × 512 + 0 × 256 + 1 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 56,000
Octal
1 5 5 3 0 0
1 × 32,768 + 5 × 4,096 + 5 × 512 + 3 × 64 + 0 × 8 + 0 × 1 = 56,000
Hexadecimal
d a c 0
d × 4,096 + a × 256 + c × 16 + 0 × 1 = 56,000
Read as powers of two: 32,768 + 16,384 + 4,096 + 2,048 + 512 + 128 + 64 = 56,000.
In historical numeral systems
Egyptian
5 fingers, 6 lotuses
5 × 10,000 + 6 × 1,000 = 56,000. 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
- Abundant number
Related numbers & connections
33.6 kbps was the limit of purely analogue modulation and 56 kbps exploited the phone network's digital core. Going faster required using the copper differently rather than improving the modem.
View 33600 →Other connections
- developed from33600
why?
Strength 0.50, confidence "high".
Technology & computing
56 kbps is close to the maximum a voice-grade channel can carry given the network's 64 kbps digital sampling. Faster access required using the copper differently rather than better modems, which is what DSL did.
DocumentedTechnology & computing
Common questions
Is 56,000 a prime number?
No, 56,000 is not prime.
What are the factors of 56,000?
The factors of 56,000 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 64, 70, 80, 100, 112, 125, 140, 160, 175, 200, 224, 250, 280, 320, 350, 400, 448, 500, 560, 700, 800, 875, 1000, 1120, 1400, 1600, 1750, 2000, 2240, 2800, 3500, 4000, 5600, 7000, 8000, 11200, 14000, 28000, 56000.
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