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50 Fun Facts About the Number 50

Updated on October 10, 2016
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TR Smith is a teacher and creator who uses mathematics in her line of work every day.

50 is an auspicious number with importance in both everyday life and higher mathematics. People celebrate milestone 50th birthdays and 50th anniversaries with more pomp than they do other year markers. Half of 100 is 50, and is a denomination of coins and paper money in many countries. When people write best-of of worst-of lists, they often try to select an even 50 items. In many ways, 50 feels complete. Here are more curious and interesting facts about the special number 50.

Nifty Fifty: Curios of the Number 50
Nifty Fifty: Curios of the Number 50

14 Math Facts About the Number 50

  • 50 is the smallest integer that can be expressed as the sum of two positive squares in two distinct ways. 49 + 1 = 25 + 25 = 50.
  • The number of letters in "fifty" equals the sum of the digits in 50. Not too many numbers have this property in English. A few other examples are 4 (four), 16 (sixteen), 36 (thirty-six), 45 (forty-five), and 83 (eighty-three).
  • 50 is also the sum of three square numbers: 3^2 + 4^2 + 5^2 = 9 + 16 + 25 = 50.
  • 50 is a Harshad number, meaning it is divisible by the sum of its digits.
  • 50^50 is an 85-digit number that ends in fifty 0s.
  • The infinitely nested radical expression sqrt(50 + sqrt(50 + sqrt(50 + ...... ))) converges to an exact value of 0.5(sqrt(201) + 1), or approximately 7.5887.
  • The geometric series 1/50 + 1/50^2 + 1/50^3 + 1/50^4 + .... converges to a value of exactly 1/49.
  • The infinite sum of reciprocals of 50th powers, 1 + 1/2^50 + 1/3^50 + 1/4^50 + ..., converges to an exact value of pi^50 times a rational number.
  • The sum of the first 50 prime numbers if 5117.
  • The sum of all the primes up to 50 is 328.
  • The 50th triangular number, i.e. the sum of all the integers from 1 to 50, is 1275.
  • The sum of the divisors (factors) of 50 is
    1 + 2 + 5 + 10 + 25 + 50 = 92.
  • There are 20 integers less than 50 that do not share any common factors with 50: 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, and 49.
  • A polygon with 50 sides is called a pentacontagon, and a polyhedron with 50 faces is called a pentacontahedron. A pentacontagon is more or less indistinguishable from a circle.

14 Facts About 50 in Culture and Science

  • The atomic number of the element tin is 50.
  • The Earth has roughly 50 times the volume of the Moon.
  • Every country has a bill or coin denominated in 50 units.
  • The 50th anniversary is known as the Golden Anniversary.
  • The 50th episode of the TV series Mad Men is titled "Chinese Wall."
  • The 50th episode of The Simpsons is titled "Homer Alone."
  • The 50th episode of the TV series Breaking Bad is titled "Fifty-One" in reference to Walter White's birthday. The series starts on the occasion of his 50th birthday.
  • The 50th episode of Seinfeld is titled "The Virgin."
  • "50 Cent" is the stage name of the rapper Curtis Jackson. This was originally the nick name of Kelvin Martin, a notorious robber from the Bronx who became known as "50 Cent" after he won $500 in a game of dice with a mere $0.50 stake.
  • If you use all seven of your letter tiles in a Scrabble play, you earn 50 extra points.
  • The word "fifty" is worth 14 points in Scrabble.
  • There are 50 states in the United States.
  • There are 11,193,770,355,829,009 ways to score exactly 50 points in a game of bowling.
  • "Five-Oh" is a slang phrase for the police. The origin of this phrase is the TV show Hawaii Five-O.

16 Miscellaneous Math Facts About 50

  • The square root of 50 is approximately 7.071.
  • There are 819 integers whose prime factors add up to 50. For example, 14076 = 2*2*3*3*17*23 and 2+2+3+3+17+23 = 50.
  • If a given amount decreases by 29.3%, and the new amount then decreases by 29.3%, you will end up with 50% of your starting amount.
  • The 50th root of 50 equals 1.0813826568. In other words, 1.0813826568^50 = 50.
  • The sum of the first 50 cube numbers 1^3 + 2^3 + 3^3 + ... + 49^3 + 50^3 is equal to 1625625. This is a curious number because not only is it a perfect square, but its digits can be partitioned into three square numbers several different ways:
    1 -- 625 -- 625
    16 -- 25 -- 625
    16 -- 256 -- 25
  • 50! (50 factorial) is a number with 65 digits that ends in 12 zeros.
  • The product of the first 50 primes (all the primes between 2 and 229 inclusive) is a number with 92 digits.
  • In binary, fifty is written as 110010.
  • In ternary, fifty is written as 1212.
  • In base-4, fifty is written as 302.
  • In base-5, fifty is written as 200.
  • In base-6, fifty is written as 242.
  • In base-φ (where φ is the golden mean) fifty can be represented either as 100000100.01000001 or as 10101110.11101101.
  • In nuclear physics, a "magic number" is a number of nucleons that can be arranged into complete shells within an atom's nucleus. The seven known magic numbers are 2, 8, 20, 28, 50, 82, and 126.
  • There are exactly 50 ways to make 50 cents using pennies (1-cent coins), nickels (5-cent coins), dimes (10-cent coins), quarters (25-cent coins), and 50 cent coins.
  • There are 50 ways to draw a square using the points of a 4x4 grid. How to generate them all is shown in the diagram below.

6 More Fun Facts About Fifty

  • 50 Shades of Grey is a popular erotic novel that started out as self-published fan-fiction based on Twilight.
  • 50 Children is a documentary about Gilbert and Eleanor Kraus, a Jewish couple from Philadelphia who took a great risk by traveling to Austria in 1939 and finding new homes in the United States for 50 Viennese Jewish children whose parents wanted them to be spared of the coming Holocaust.
  • 50 First Dates is a romantic comedy about a woman with severe anterograde amnesia. It is one of the very few non-terrible Adam Sandler movies.
  • In Roman numerals, fifty is L.
  • The book of Genesis in the Bible has 50 chapters.
  • Priam, the mythical Troy king, had 50 more sons than daughters -- 68 sons and 18 daughters.

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    • jabelufiroz profile image

      Firoz 3 years ago from India

      Well researched article. Voted up.

    • calculus-geometry profile image
      Author

      TR Smith 3 years ago from Germany

      Thanks, glad you liked it!

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