220 (number)
| ||||
|---|---|---|---|---|
| Cardinal | two hundred twenty | |||
| Ordinal |
220th (two hundred and twentieth) | |||
| Factorization | 22× 5 × 11 | |||
| Roman numeral | CCXX | |||
| Binary | 110111002 | |||
| Ternary | 220113 | |||
| Quaternary | 31304 | |||
| Quinary | 13405 | |||
| Senary | 10046 | |||
| Octal | 3348 | |||
| Duodecimal | 16412 | |||
| Hexadecimal | DC16 | |||
| Vigesimal | B020 | |||
| Base 36 | 6436 | |||
220 (two hundred [and] twenty) is the natural number following 219 and preceding 221.
In mathematics
It is a composite number, with its divisors being 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, making it an amicable number with 284.[1][2] Every number up to 220 may be expressed as a sum of its divisors, making 220 a practical number.[3] Also, being divisible by the sum of its digits, 220 is a Harshad number.[4]
It is the sum of four consecutive primes (47 + 53 + 59 + 61).[5] It is the smallest even number with the property that when represented as a sum of two prime numbers (per Goldbach's conjecture) both of the primes must be greater than or equal to 23.[6] There are exactly 220 different ways of partitioning 64 = 82 into a sum of square numbers.[7]
It is a tetrahedral number, the sum of the first ten triangular numbers,[8] and a dodecahedral number.[9] If all of the diagonals of a regular decagon are drawn, the resulting figure will have exactly 220 regions.[10]
It is the sum of the sums of the divisors of the first 16 positive integers.[11]
In other fields
The number 220 can also refer to:
- The years 220 AD and 220 BC.
- A common voltage in many countries.
- An SMTP code meaning "service ready"
- A series of garden tractors produced by Case (and later by Case IH) in the 1970s and 1980s - the series included the 220(10HP), the 222(12HP) and the 224(14HP).
- 220 film, a film format for medium format cameras.
- A single by music duo t.A.T.u.
- An album by guitarist Phil Keaggy.
- The InterCity 225 train, a newer version of the InterCity 125.
- .220 Russian and .220 Swift, firearm cartridges
Notes
- ↑ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 167
- ↑ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
- ↑ "Sloane's A005153 : Practical numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A005349 : Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A034963 : Sums of four consecutive primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A025018 : Numbers n such that least prime in Goldbach partition of n increases". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A037444 : Number of partitions of n^2 into squares". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A000292 : Tetrahedral (or triangular pyramidal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A006566 : Dodecahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A007678 : Number of regions in regular n-gon with all diagonals drawn". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Sloane's A024916 : sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
References
- Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 145 – 147). London: Penguin Group.