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Easily one of the most interesting numbers I can think of.
This is largely due to the fact that 153 is the sum or product of other interesting numbers. Also, imho, 153 is at least as interesting as 23, which is widely known to be the smallest interesting number.


The Basics:


The Interesting Stuff:

  • 153 is the smallest number - other than 1 - which can be expressed as the sum of cubes of its digits:

    153 = 13 + 53 + 33.

    See also: Narcissistic number.


  • It is equal to the sum of the first 5 factorials:

    153 = 1! + 2! + 3! + 4! + 5!



  • The sum of digits of 153 is a perfect square:

    1 + 5 + 3 = 9 = 32



  • On adding the number 153 to its reverse, 504 is obtained, which when squared is the smallest square which can be expressed as the product of two different numbers which are reverse of one another:

    153 + 351 = 504

    5042 = 288 x 882 (= 254016)



  • It is the 17th triangular number: it is the sum of all integers from 1 to 17. Since reverse of 153, i.e. 351 is also a triangular number, 153 can be termed as a reversible triangular number.


  • Its prime factorization is 153 = 32 x 17. 32 = 9 = 1 + 5 + 3, meaning that 153 is divisible by the sum of its digits. This qualifies it as one of the illustrious Harshad numbers (a.k.a. Niven number).


  • It can be expressed as the product of two numbers formed from its own digits:

    153 = 3 * 51



  • 153 is the 9th hexagonal number. Hexagonal numbers are given by the formula H(n) = n(2n - 1).


  • If all 6 combinations of number 1, 5, 3 are taken to form a three digit number then the following is true:

    153 + 315 + 531 = 351 + 135 + 513

    10 + 51 + 32 = 1 * 5 * 3


But the weirdest, wonderfullest, wackiest fact-about-a-number for today:
  • Work out its reciprocal

    1/153 = 0.006535947712418300653594...

    Multiplying all the significant figures (the repeated non-zero numbers after the point) by 17, and multiples of 17 the pattern generated is:

    65359477124183 x 17 = 1111111111111111

    65359477124183 x 34 = 2222222222222222

    65359477124183 x 51 = 3333333333333333

    65359477124183 x 68 = 4444444444444444

    65359477124183 x 85 = 5555555555555555

    65359477124183 x 102 = 6666666666666666

    65359477124183 x 119 = 7777777777777777

    65359477124183 x 136 = 8888888888888888

    65359477124183 x 153 = 9999999999999999


Fairly Interesting Biblical Stuff©:

  • 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.

  • The number of fish caught by Simon Peter:
    “Simon Peter went up, and drew the net to land full of great fishes, an hundred and fifty and three: and for all there were so many, yet was not the net broken”. -King James Bible, John 21:11

wikipedia.org
worldofnumbers.com/em41.htm
shyamsundergupta.com/c153.htm

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