220 (number)

Short description: Natural number

| <- 219  | 220 |  221 ->

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← 220 221 222 223 224 225 226 227 228 229 →

List of numbers — Integers

← 0 100 200 300 400 500 600 700 800 900 →

Cardinal| two hundred twenty
Ordinal| 220th
(two hundred twentieth)
Factorization| 22 × 5 × 11
Greek numeral| ΣΚ´
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.

## Contents

* 1 In mathematics
* 2 Integers between 221 and 229
* 2.1 221
* 2.2 222
* 2.3 223
* 2.4 224
* 2.5 225
* 2.6 226
* 2.7 227
* 2.8 228
* 2.9 229
* 3 Notes
* 4 References

## In mathematics

It is a composite number, with its proper 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]

It is the sum of four consecutive primes (47 + 53 + 59 + 61).[4] 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.[5] There are exactly 220 different ways of partitioning 64 = 82 into a sum of square numbers.[6]

It is a tetrahedral number, the sum of the first ten triangular numbers,[7] and a dodecahedral number.[8] If all of the diagonals of a regular decagon are drawn, the resulting figure will have exactly 220 regions.[9]

It is the sum of the sums of the divisors of the first 16 positive integers.[10]

## Integers between 221 and 229

### 221

Main article: 221 (number)

### 222

Main article: 222 (number)

### 223

Main article: 223 (number)

### 224

Main article: 224 (number)

### 225

Main article: 225 (number)

### 226

Main article: 226 (number)

### 227

Main article: 227 (number)

### 228

Main article: 228 (number)

### 229

Main article: 229 (number)

## Notes

1. ↑ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 167
2. ↑ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1. https://archive.org/details/numberstoryfromc00higg_612.
3. ↑ Sloane, N. J. A., ed. "Sequence A005153 (Practical numbers)". OEIS Foundation. https://oeis.org/A005153.
4. ↑ Sloane, N. J. A., ed. "Sequence A034963 (Sums of four consecutive primes)". OEIS Foundation. https://oeis.org/A034963.
5. ↑ Sloane, N. J. A., ed. "Sequence A025018 (Numbers n such that least prime in Goldbach partition of n increases)". OEIS Foundation. https://oeis.org/A025018.
6. ↑ Sloane, N. J. A., ed. "Sequence A037444 (Number of partitions of n^2 into squares)". OEIS Foundation. https://oeis.org/A037444.
7. ↑ Sloane, N. J. A., ed. "Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers)". OEIS Foundation. https://oeis.org/A000292.
8. ↑ Sloane, N. J. A., ed. "Sequence A006566 (Dodecahedral numbers)". OEIS Foundation. https://oeis.org/A006566.
9. ↑ Sloane, N. J. A., ed. "Sequence A007678 (Number of regions in regular n-gon with all diagonals drawn)". OEIS Foundation. https://oeis.org/A007678.
10. ↑ Sloane, N. J. A., ed. "Sequence A024916 (sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)". OEIS Foundation. https://oeis.org/A024916.

## References

* Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 145 – 147). London: Penguin Group.

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