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| Cardinal
| eight thousand one hundred [and] twenty-eight
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| Ordinal
| 8128th (eight thousand one hundred [and] twenty-eighth)
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| Factorization
| $2^6\; cdot\; 127$
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| Divisors
| 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064
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| Roman numeral
| $overline\{mbox\{VIII\}\}mbox\{CXXVIII\}$
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| Binary
| 1111111000000
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| Octal
| 17700
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| Duodecimal
| 4854
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| Hexadecimal
| 1FC0
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'8128' is the natural number following 8127 and preceding 8129.
It is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 127, 2⁷ − 1, with 2⁶ ( 2⁷ − 1 ) yielding 8128. Also related to its being a perfect number, 8128 is a harmonic divisor number.
Another consequence of 8128 being a perfect number is that it has the same prime factors as the sum of its divisors, its cototient is a power of two, and it is a harmonic seed number (though there are deficient and abundant numbers that share these properties).
8128 is the 127th triangular number, the 64th hexagonal number, the eighth 292-gonal number, and the fourth 1356-gonal number, as well as a centered nonagonal number.

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See also

See also

★ 8128 Nicomachus