8128 (number)

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Cardinal	eight thousand one hundred and twenty-eight
Ordinal	8128th (eight thousand one hundred and twenty-eighth)
Factorization	$2^6 \cdot 127$
Divisors	2, 4, 8, 11, 16, 22, 32, 44, 64, 127, 254, 508, 1,016, 2,032, 4,064
Roman numeral	$\overline\mbox{VIII}\mbox{CXXVIII}$
Binary	1111111000000
Octal	17700
Duodecimal	4854
Hexadecimal	1FC0

8,128 is the natural number following 8,127 and preceding 8,129. 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 8,128. Also related to its being a perfect number, 8,128 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). One property that 8128 doesn't share with all the other perfect numbers is that it is the sum of every fourth entry of a row in Pascal's triangle. 8,128 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.

8128 (Number)

See also