# 50 (number)

50 (fifty) is the natural number following 49 and preceding 51.

 ← 49 50 51 →
Cardinalfifty
Ordinal50th
(fiftieth)
Numeral systemquinquagesimal
Factorization2 × 52
Divisors1, 2, 5, 10, 25, 50
Greek numeralΝ´
Roman numeralL
Unicode symbol(s)
Binary1100102
Ternary12123
Senary1226
Octal628
Duodecimal4212

## In mathematics

Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways: 50 = 12 + 72 = 52 + 52.[1] It is also the sum of three squares, 50 = 32 + 42 + 52, and the sum of four squares, 50 = 62 + 32 + 22 + 12. It is a Harshad number.[2]

50 is a Stirling number of the first kind: ${\displaystyle \left[{5 \atop 2}\right]=50}$ , and also a Narayana number: ${\displaystyle \operatorname {N} (6,3)=\operatorname {N} (6,4)=50}$

There is no solution to the equation φ(x) = 50, making 50 a nontotient.[3] Nor is there a solution to the equation x − φ(x) = 50, making 50 a noncototient.[4]

## In other fields

Fifty is:

• There are 50 states in the United States of America.
• The TV show Hawaii Five-O and its reimagined version, Hawaii Five-0, are so called because Hawaii is the last (50th) of the states to officially become a state.
• 5-O (Five-Oh) - Slang for police officers and/or a warning that police are approaching. Derived from the television show Hawaii Five-O[6]
• A calibre of ammunition (0.50 inches: see .50 BMG)
• In millimetres, the focal length of the normal lens in 35 mm photography
• The percentage (50%) equivalent to one half, so that the phrase "fifty-fifty" commonly expresses something divided equally in two; in business this is often denoted as being the ultimate in equal partnership
• In years of marriage, the gold or "golden" wedding anniversary
• The speed limit, in kilometres per hour, of Australian and Canadian roads with unspecified limits.

## References

1. ^ de Koninck, J.M. (2009). Those fascinating numbers. AMS Bookstore. p. 18. ISBN 0-8218-4807-0.
2. ^ "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. ^ "Sloane's A005277 : Nonients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. ^ "Sloane's A005278 : Noncotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. ^ Leviticus 25:10
6. ^ Karen Rhodes (1 February 1997). Booking Hawaii Five-O: An Episode Guide and Critical History of the 1968–1980 Television Detective Series. McFarland. p. 265. ISBN 978-0-7864-8666-3.