71,000
71000 Duke of Gloucester was Britain's last express passenger steam locomotive.
- Even
- Composite
Where 71,000 fits
Why 71,000 is special
It performed poorly in service, and preservation later showed the fault lay in manufacturing errors rather than in the design.
Factors & digit properties
- Divisors (32)
- 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 71, 100, 125, 142, 200, 250, 284, 355, 500, 568, 710, 1000, 1420, 1775, 2840, 3550, 7100, 8875, 14200, 17750, 35500, 71000
- Prime factorisation
- 2^3 × 5^3 × 71
- Digit sum
- 8
- Digital root
- 8
Representations
- Decimal
- 71000
- Scientific notation
- 7.100 × 10^4
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0
1 × 65,536 + 0 × 32,768 + 0 × 16,384 + 0 × 8,192 + 1 × 4,096 + 0 × 2,048 + 1 × 1,024 + 0 × 512 + 1 × 256 + 0 × 128 + 1 × 64 + 0 × 32 + 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 71,000
Octal
2 1 2 5 3 0
2 × 32,768 + 1 × 4,096 + 2 × 512 + 5 × 64 + 3 × 8 + 0 × 1 = 71,000
Hexadecimal
1 1 5 5 8
1 × 65,536 + 1 × 4,096 + 5 × 256 + 5 × 16 + 8 × 1 = 71,000
Read as powers of two: 65,536 + 4,096 + 1,024 + 256 + 64 + 16 + 8 = 71,000.
In historical numeral systems
Egyptian
7 fingers, 1 lotus
7 × 10,000 + 1 × 1,000 = 71,000. 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
- Harshad (Niven) number
Related numbers & connections
Both were built for British Railways in the 1950s, and both had working lives far shorter than their designs intended.
View 92220 →Other connections
- is associated with92220
why?
Strength 0.50, confidence "high".
History
71000 Duke of Gloucester was built in 1954 and withdrawn in 1962 with a reputation for poor steaming. Restoration identified incorrectly made draughting components, after which performance improved markedly.
DocumentedHistoryGeography: United KingdomPeriod: 1954–1962
Common questions
Is 71,000 a prime number?
No, 71,000 is not prime.
What are the factors of 71,000?
The factors of 71,000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 71, 100, 125, 142, 200, 250, 284, 355, 500, 568, 710, 1000, 1420, 1775, 2840, 3550, 7100, 8875, 14200, 17750, 35500, 71000.
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