224 (number)

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

Contents

In mathematics

223 224 225
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
Senary 10126
Octal 3408
Duodecimal 16812
Hexadecimal E016

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] That distinction now belongs to 315.

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

Related Research Articles

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<span class="mw-page-title-main">1,000,000</span> Natural number

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<span class="mw-page-title-main">1,000,000,000</span> Natural number

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216 is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.

225 is the natural number following 224 and preceding 226.

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189 is the natural number following 188 and preceding 190.

20,000 is the natural number that comes after 19,999 and before 20,001.

30,000 is the natural number that comes after 29,999 and before 30,001.

40,000 is the natural number that comes after 39,999 and before 40,001. It is the square of 200.

50,000 is the natural number that comes after 49,999 and before 50,001.

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References

  1. Sloane, N. J. A. (ed.). "SequenceA005153(Practical numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. Sloane, N. J. A. (ed.). "SequenceA003325(Numbers that are the sum of 2 positive cubes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. Sloane, N. J. A. (ed.). "SequenceA003998(Numbers that are a sum of distinct positive cubes in more than one way)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. Sloane, N. J. A. (ed.). "SequenceA141162(Smallest k such that lambda(k) = n)". The On-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. Retrieved 2023-03-09.
  7. Housley, R. (September 2004). "RFC 3874: A 224-bit One-way Hash Function: SHA-224". Network Working Group. Retrieved 2023-03-09.
  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.