170 (number)

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← 169 170 171 →
Cardinal one hundred seventy
Ordinal 170th
(one hundred seventieth)
Factorization 2 × 5 × 17
Divisors 1, 2, 5, 10, 17, 34, 85, 170
Greek numeral ΡΟ´
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, N.J.A. (ed.). "Sequence 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]