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224 (number)

From Wikipedia, the free encyclopedia

224 (two hundred [and] twenty-four) is the natural number following223 and preceding225.

In mathematics

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Natural number
← 223224 225 →
Cardinaltwo hundred twenty-four
Ordinal224th
(two hundred twenty-fourth)
Factorization25 × 7
PrimeNo
Greek numeralΣΚΔ´
Roman numeralCCXXIV,ccxxiv
Binary111000002
Ternary220223
Senary10126
Octal3408
Duodecimal16812
HexadecimalE016

224 is apractical number,[1]and a sum of two positive cubes23 + 63.[2] It is also23 + 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 smallestk with λ(k) = 24, where λ(k) is theCarmichael function.[4]

The mathematician and philosopherAlex Bellos suggested in 2014 that a candidate for the lowestuninteresting 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] (As of August 2025, that distinction was held by 317.)

In other areas

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In theSHA-2 family of sixcryptographic 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-keyTriple DES.[7]

The ancient Phoenicianshekel was a standardized measure ofsilver, 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 ancientBurma andThailand, silver was measured in a unit called atikal, equal to 224 grains.[9]

See also

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References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A005153 (Practical numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Sloane, N. J. A. (ed.)."Sequence A003325 (Numbers that are the sum of 2 positive cubes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A003998 (Numbers that are a sum of distinct positive cubes in more than one way)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Sloane, N. J. A. (ed.)."Sequence A141162 (Smallest k such that lambda(k) = n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  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)"(PDF). NIST. February 25, 2004. Retrieved2023-03-09.
  7. ^Housley, R. (September 2004)."RFC 3874: A 224-bit One-way Hash Function: SHA-224". Network Working Group. Retrieved2023-03-09.
  8. ^Bratcher, Robert G. (October 1959). "Weights, Money, Measures and Time".The Bible Translator.10 (4). {SAGE} Publications:165–174.doi:10.1177/000608445901000404.S2CID 125756547.
  9. ^Cunningham, Alexander (1891).Coins of Ancient India: From the Earliest Times Down to the Seventh Century A.D. London: B. Quaritch. p. 4.
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