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170 (number)

← 169 170 171 →
Cardinalone hundred seventy
Ordinal170th
(one hundred seventieth)
Factorization2 × 5 × 17
Divisors1, 2, 5, 10, 17, 34, 85, 170
Greek numeralΡΟ´
Roman numeralCLXX
Binary101010102
Ternary200223
Senary4426
Octal2528
Duodecimal12212
HexadecimalAA16

170 (one hundred [and] 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 × 10306.[citation needed]

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]

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.
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