170 (number)

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169 170 171
Cardinal one hundred and seventy
Ordinal 170th
(one hundred and seventieth)
Factorization 2 · 5 · 17
Divisors 1, 2, 5, 10, 17, 34, 85, 170
Roman numeral CLXX
Binary 101010102
Ternary 200223
Quaternary 22224
Quinary 11405
Senary 4426
Octal 2528
Duodecimal 12212
Hexadecimal AA16
Vigesimal 8A20
Base 36 4Q36

170 (one hundred [and] seventy) is the natural number following 169 and preceding 171.

In mathematics[edit]

170 is the smallest n for which φ(n) and σ(n) are both square(64 and 324 respectively). But 170 is never a solution for φ(x), making it a nontotient. Nor is it ever a solution to x - φ(x), making it a noncototient.

170 is a repdigit in base 4 (2222) and base 16 (AA), as well as in bases 33, 84, and 169. It is also a sphenic number.

170 is the largest integer for which its factorial can be stored in double-precision floating-point format. This is probably why it is also the largest factorial that Google's built-in calculator will calculate, returning the answer as 170! = 7.25741562 × 10306.

There are 170 different cyclic Gilbreath permutations on 12 elements,[1] and therefore there are 170 different real periodic points of order 12 on the Mandelbrot set.[2]

In sports[edit]

  • 170 is the maximum check-out possible in a standard game of darts (where the final score must be a double). It consists of two treble-twenties and a double-bullseye.[3]

See also[edit]

References[edit]

  1. ^ "Sloane's A000048 ", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Diaconis, Persi; Graham, Ron (2012), "Chapter 5: From the Gilbreath Principle to the Mandelbrot Set", Magical Mathematics: the mathematical ideas that animate great magic tricks, Princeton University Press, pp. 61–83 .
  3. ^ Rushin, Steve (2007), The Caddie Was a Reindeer: And Other Tales of Extreme Recreation, Grove Press, p. 79, ISBN 9781555847333 .

External links[edit]