224 (number)

224 (two hundred [and] twenty-four) is the natural number following 223 and preceding 225.

## Contents

* 1 In mathematics
* 2 In other areas
* 3 See also
* 4 References

## In mathematics

Short description: Natural number

| <- 223  | 224 |  225 ->

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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-four
Ordinal| 224th
(two hundred twenty-fourth)
Factorization| 25 × 7
Prime| No
Greek numeral| ΣΚΔ´
Roman numeral| CCXXIV
Binary| 111000002
Ternary| 220223
Quaternary| 32004
Quinary| 13445
Senary| 10126
Octal| 3408
Duodecimal| 16812
Hexadecimal| E016
Vigesimal| B420
Base 36| 6836

224 is a practical number,[1] and a sum of two positive cubes 23 \+ 63.[2] It is also 23 \+ 33 \+ 43 \+ 53, making it one of the smallest numbers to be the sum of distinct positive cubes in more than one way.[3]

224 is the smallest k with λ(k) = 24, where λ(k) is the Carmichael function.[4]

The mathematician and philosopher Alex Bellos suggested in 2014 that a candidate for the lowest uninteresting number would be 224 because it was, at the time, "the lowest number not to have its own page on [the English-language version of] Wikipedia".[5]

## In other areas

In the SHA-2 family of six cryptographic hash functions, the weakest is SHA-224, named because it produces 224-bit hash values.[6] It was defined in this way so that the number of bits of security it provides (half of its output length, 112 bits) would match the key length of two-key Triple DES.[7]

The ancient Phoenician shekel was a standardized measure of silver, equal to 224 grains, although other forms of the shekel employed in other ancient cultures (including the Babylonians and Hebrews) had different measures.[8] Likely not coincidentally, as far as ancient Burma and Thailand, silver was measured in a unit called a tikal, equal to 224 grains.[9]

## See also

* 224 (disambiguation)

## References

1. ↑ Sloane, N. J. A., ed. "Sequence A005153 (Practical numbers)". OEIS Foundation. https://oeis.org/A005153.
2. ↑ Sloane, N. J. A., ed. "Sequence A003325 (Numbers that are the sum of 2 positive cubes)". OEIS Foundation. https://oeis.org/A003325.
3. ↑ Sloane, N. J. A., ed. "Sequence A003998 (Numbers that are a sum of distinct positive cubes in more than one way)". OEIS Foundation. https://oeis.org/A003998.
4. ↑ Sloane, N. J. A., ed. "Sequence A141162 (Smallest k such that lambda(k) = n)". OEIS Foundation. https://oeis.org/A141162.
5. ↑ Bellos, Alex (June 2014). The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life. illus. The Surreal McCoy (1st Simon & Schuster hardcover ed.). N.Y.: Simon & Schuster. pp. 238 & 319 (quoting p. 319). ISBN 978-1-4516-4009-0.
6. ↑ "FIPS Publication 180-2 (with Change Notice 1): Announcing the Secure Hash Standard (+ Change Notice to Include SHA-224)". NIST. February 25, 2004. https://csrc.nist.gov/csrc/media/publications/fips/180/2/archive/2002-08-01/documents/fips180-2withchangenotice.pdf.
7. ↑ Housley, R. (September 2004). "RFC 3874: A 224-bit One-way Hash Function: SHA-224". Network Working Group. https://datatracker.ietf.org/doc/html/rfc3874.
8. ↑ Bratcher, Robert G. (October 1959). "Weights, Money, Measures and Time". The Bible Translator ({SAGE} Publications) 10 (4): 165–174. doi:10.1177/000608445901000404.
9. ↑ Cunningham, Alexander (1891). Coins of Ancient India: From the Earliest Times Down to the Seventh Century A.D.. London: B. Quaritch. p. 4. https://archive.org/details/coinsancientind00cunngoog.

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