153 (number)

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153
Ordinal 153
Cardinal 153rd
Factorization 153 = 3^2 \cdot 17
Divisors 1, 3, 9, 17, 51, 153
Roman numeral CLIII
Binary 10011001
Octal 231
Hexadecimal 99

One hundred (and) fifty-three is the natural number following one hundred (and) fifty-two and preceding one hundred (and) fifty-four.

As a triangular number, it is the sum of the first 17 integers, and also the sum of the first five positive factorials. It is also a hexagonal number. It is also one of six known truncated triangle numbers, meaning 1, 15, and 153 are all triangle numbers

The distinct prime factors of 153 add up to 20, and so do the ones of 154, hence the two form a Ruth-Aaron pair.

Another interesting feature of the number 153 is that it's the limit of the following algorithm:

  1. Take a random positive integer, divisible by three.
  2. Split that number into its base 10 digits.
  3. Take the sum of their cubes.
  4. Go to the second step.

An example, starting with the number 84:

83 + 43 = 512 + 64 = 576
53 + 73 + 63 = 125 + 343 + 216 = 684
63 + 83 + 43 = 216 + 512 + 64 = 792
73 + 93 + 23 = 343 + 729 + 8 = 1080
13 + 03 + 83 + 03 = 1 + 0 + 512 + 0 = 513
53 + 13 + 33 = 125 + 1 + 27 = 153
13 + 53 + 33 = 1 + 125 + 27 = 153

Evagrius Ponticus considered 153 to represent a harmonization of contrasts, since 153 = 100 + 28 + 25, with 100 representing a square, 28 a triangle and 25 a circle.

Since 153 = 13 + 53 + 33, it is a 3-narcissistic number, and it is a Friedman number since 153 = 3 * 51. It is a Harshad number in base 10.

153 can also be written as 1! + 2! + 3! + 4! + 5!.

Contents

[edit] Other usages

  • The original price, in US Dollars, of the diet pill Leptoprin, marketed by the slogan "When is a diet pill worth $153 a bottle?"
  • The number of fish caught in the Catch of 153 fish in the biblical narrative of the Gospel of John (see Gospel of John chapter 21, verse 11)
  • The number of combined Arabic and Persian Hidden Words in the Bahá'í Faith.
  • Considered by St. Augustine to represent seven gifts of the Holy Spirit and ten requirements of God.
  • The frequency of the longwave transmitters Donebach, Ingoy and Braşov in kilohertz.
  • The ordinal number of the coat of arms of Komi Republic in the State Heraldic Register of the Russian Federation.
  • Any five consecutive months in the Gregorian calendar that do not include February total 153 days.
  • The number of aphorisms outlined by Chr. Pack in 1687-88 in this printed work: One hundred fifty three chymical aphorisms. Briefly containing whatsoever belongs to the chymical science. Done by the labour and study of Eremita Suburbanus. Printed in Latin at Amsterdam, Octob. 1687. To which are added, some other phylosophick canons or rules pertaining to the Hermetick science. Made English and published for the sake of the sedulous labourers in true chymistry... by Chr. Packe. London: for the author, sold by W. Cooper. 1688. The book seems to be focused upon alchemy.

[edit] See also

For the year, see AD 153.

[edit] References

  • Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 140 - 141

[edit] External links