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170 (number)

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Natural number
← 169 170 171 →
170 171 172 173 174 175 176 177 178 179 0 100 200 300 400 500 600 700 800 900
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 seventy) is the natural number following 169 and preceding 171.

In mathematics

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 IEEE 754 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 × 10.

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

See also

References

  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.

External links

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