8,128
8128 is the fourth perfect number: it equals the sum of its proper divisors.
- Even
- Composite
Where 8,128 fits
Why 8,128 is special
8128 was the last perfect number known to the ancient world, and it sat there for a very long time — the fifth, 33,550,336, was not recorded until the fifteenth century. It follows 6, 28 and 496, fits Euclid's construction as 2⁶ × (2⁷ − 1) with 127 prime, and like every known perfect number it is even.
8,128 is part of
Factors & digit properties
- Divisors (14)
- 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064, 8128
- Prime factorisation
- 2^6 × 127
- Digit sum
- 19
- Digital root
- 1
Representations
- Decimal
- 8128
- Binary
- 1111111000000
- Octal
- 17700
- Hexadecimal
- 1fc0
- Scientific notation
- 8.128 × 10^3
Other mathematical patterns
- Triangular number
- Perfect number
- Happy number
- Hexagonal number
Related numbers & connections
The third and fourth perfect numbers, and the last two the ancient world knew. Both follow Euclid's construction from a Mersenne prime, and the gap after 8128 lasted well over a thousand years before the fifth was recorded.
View 496 →Numbers Around Us
- appears alongside496
why?
Strength 0.50, confidence "high".
History
6, 28, 496 and 8128 were all known in antiquity and appear in Nicomachus. The fifth perfect number, 33,550,336, was not recorded until the fifteenth century — a gap of well over a thousand years, because finding it meant testing whether a much larger Mersenne candidate is prime, which is hard without notation and mechanical calculation.
DocumentedHistoryPeriod: antiquity – 15th century
Common questions
Is 8,128 a prime number?
No, 8,128 is not prime.
What are the factors of 8,128?
The factors of 8,128 are 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064, 8128.
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: 3 August 2026