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170 (number)

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Natural number
← 169170 171 →
Cardinalone hundred seventy
Ordinal170th
(one hundred seventieth)
Factorization2 × 5 × 17
Divisors1, 2, 5, 10, 17, 34, 85, 170
Greek numeralΡΟ´
Roman numeralCLXX,clxx
Binary101010102
Ternary200223
Senary4426
Octal2528
Duodecimal12212
HexadecimalAA16

170 (one hundred [and] seventy) is thenatural number following169 and preceding171.

In mathematics

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170 is the smallestn 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 anontotient. Nor is it ever a solution tox - φ(x), making it anoncototient.

170 is arepdigit inbase 4 (2222) andbase 16 (AA), as well as in bases 33, 84, and 169. It is also asphenic number.

170 is the largest integer for which itsfactorial can be stored inIEEE 754 double-precision floating-point format. This is probably why it is also the largestfactorial thatGoogle's built-incalculator will calculate, returning the answer as 170! = 7.25741562 × 10306.[citation needed]

There are 170 differentcyclicGilbreath permutations on 12 elements,[1] and therefore there are 170 differentreal periodic points of order 12 on theMandelbrot set.[2]

References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A000048".TheOn-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.

External links

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