# 84 (number)

(Redirected from Eighty-four)
 ← 83 84 85 →
Cardinaleighty-four
Ordinal84th
(eighty-fourth)
Factorization22 × 3 × 7
Divisors1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Greek numeralΠΔ´
Roman numeralLXXXIV
Binary10101002
Ternary100103
Senary2206
Octal1248
Duodecimal7012

84 (eighty-four) is the natural number following 83 and preceding 85.

## In mathematics

84 is a semiperfect number,[1] being thrice a perfect number, and the sum of the sixth pair of twin primes ${\displaystyle (41+43)}$.[2] It is the number of four-digit perfect powers in decimal.[3]

It is the third (or second) dodecahedral number,[4] and the sum of the first seven triangular numbers (1, 3, 6, 10, 15, 21, 28, 36), which makes it the sixth tetrahedral number.[5]

The twenty-second unique prime in decimal, with notably different digits than its preceding (and known following) terms in the same sequence, contains a total of 84 digits.[6]

A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces.

84 is the limit superior of the largest finite subgroup of the mapping class group of a genus ${\displaystyle g}$ surface divided by ${\displaystyle g}$.[citation needed]

Under Hurwitz's automorphisms theorem, a smooth connected Riemann surface ${\displaystyle X}$ of genus ${\displaystyle g>1}$ will contain an automorphism group ${\displaystyle \mathrm {Aut} (X)=G}$ whose order is classically bound to ${\displaystyle |G|\leq 84{\text{ }}(g-1)}$.[7]

There are 84 zero divisors in the 16-dimensional sedenions ${\displaystyle \mathbb {S} }$.[8]

## In other fields

Eighty-four is also: