33,600
33,600 bits per second was the last modem speed before the 56k ceiling.
- Even
- Composite
Where 33,600 fits
Why 33,600 is special
V.34 was refined to reach it in 1996, a year before 56k arrived and two before broadband began displacing dial-up entirely. It marks the end of the analogue modem's development.
Factors & digit properties
- Divisors (84)
- 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 64, 70, 75, 80, 84, 96, 100, 105, 112, 120, 140, 150, 160, 168, 175, 192, 200, 210, 224, 240, 280, 300, 320, 336, 350, 400, 420, 448, 480, 525, 560, 600, 672, 700, 800, 840, 960, 1050, 1120, 1200, 1344, 1400, 1600, 1680, 2100, 2240, 2400, 2800, 3360, 4200, 4800, 5600, 6720, 8400, 11200, 16800, 33600
- Prime factorisation
- 2^6 × 3 × 5^2 × 7
- Digit sum
- 12
- Digital root
- 3
Representations
- Decimal
- 33600
- Scientific notation
- 3.360 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0
1 × 32,768 + 0 × 16,384 + 0 × 8,192 + 0 × 4,096 + 0 × 2,048 + 0 × 1,024 + 1 × 512 + 1 × 256 + 0 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 33,600
Octal
1 0 1 5 0 0
1 × 32,768 + 0 × 4,096 + 1 × 512 + 5 × 64 + 0 × 8 + 0 × 1 = 33,600
Hexadecimal
8 3 4 0
8 × 4,096 + 3 × 256 + 4 × 16 + 0 × 1 = 33,600
Read as powers of two: 32,768 + 512 + 256 + 64 = 33,600.
In historical numeral systems
Egyptian
3 fingers, 3 lotuses, 6 coils of rope
3 × 10,000 + 3 × 1,000 + 6 × 100 = 33,600. 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
- Harshad (Niven) 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 56000 →Other connections
- developed from56000
why?
Strength 0.50, confidence "high".
Technology & computing
33.6 kbps in 1996 was the practical limit of purely analogue modulation. Everything faster required exploiting the phone network's digital core rather than improving the modem.
DocumentedTechnology & computingPeriod: 1996
Common questions
Is 33,600 a prime number?
No, 33,600 is not prime.
What are the factors of 33,600?
The factors of 33,600 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 64, 70, 75, 80, 84, 96, 100, 105, 112, 120, 140, 150, 160, 168, 175, 192, 200, 210, 224, 240, 280, 300, 320, 336, 350, 400, 420, 448, 480, 525, 560, 600, 672, 700, 800, 840, 960, 1050, 1120, 1200, 1344, 1400, 1600, 1680, 2100, 2240, 2400, 2800, 3360, 4200, 4800, 5600, 6720, 8400, 11200, 16800, 33600.
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