84 (eighty-four) is the natural number following 83 and preceding 85.
| ||||
---|---|---|---|---|
Cardinal | eighty-four | |||
Ordinal | 84th (eighty-fourth) | |||
Factorization | 22 × 3 × 7 | |||
Divisors | 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 | |||
Greek numeral | ΠΔ´ | |||
Roman numeral | LXXXIV | |||
Binary | 10101002 | |||
Ternary | 100103 | |||
Senary | 2206 | |||
Octal | 1248 | |||
Duodecimal | 7012 | |||
Hexadecimal | 5416 |
84 is a semiperfect number,[1] being thrice a perfect number, and the sum of the sixth pair of twin primes .[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 surface divided by .[citation needed]
Under Hurwitz's automorphisms theorem, a smooth connected Riemann surface of genus will contain an automorphism group whose order is classically bound to .[7]
84 is the thirtieth and largest for which the cyclotomic field has class number (or unique factorization), preceding 60 (that is the composite index of 84),[8] and 48.[9][10]
There are 84 zero divisors in the 16-dimensional sedenions .[11]
Eighty-four is also: