80 (number)
Natural number
From Wikipedia, the free encyclopedia
80 (eighty) is the natural number following 79 and preceding 81.
| ||||
|---|---|---|---|---|
| Cardinal | eighty | |||
| Ordinal | 80th (eightieth) | |||
| Numeral system | octogesimal | |||
| Factorization | 24 × 5 | |||
| Divisors | 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 (10) | |||
| Greek numeral | Π´ | |||
| Roman numeral | LXXX, lxxx | |||
| Binary | 10100002 | |||
| Ternary | 22223 | |||
| Senary | 2126 | |||
| Octal | 1208 | |||
| Duodecimal | 6812 | |||
| Hexadecimal | 5016 | |||
| Armenian | Ձ | |||
| Hebrew | פ / ף | |||
| Babylonian numeral | 𒐕⟪ | |||
| Egyptian hieroglyph | 𓎍 | |||
In mathematics
80 is:
- The sum of Euler's totient function φ(x) over the first sixteen integers:
- 1 + 1 + 2 + 2 + 4 + 2 + 6 + 4 + 6 + 4 + 10 + 4 + 12 + 6 + 8 + 8 = 80.
- A semiperfect number, since adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20, and 40) gives 80.[1]
- A ménage number.[2]
- Palindromic in bases 3 (22223), 6 (2126), 9 (889), 15 (5515), 19 (4419), and 39 (2239).
- A repdigit in bases 3, 9, 15, 19, and 39.
- The sum of the first four twin prime pairs:
- (3 + 5) + (5 + 7) + (11 + 13) + (17 + 19) = 80.
The Pareto principle (also known as the 80-20 rule) states that, for many events, roughly 80% of the effects come from 20% of the causes.[3][4]
Every solvable configuration of the 15 puzzle can be solved in no more than 80 single-tile moves.[5]
