109 (number)

Short description: Natural number

← 108 109 110 →
← 100 101 102 103 104 105 106 107 108 109 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred nine
Ordinal	109th (one hundred ninth)
Factorization	prime
Prime	29th
Divisors	1, 109
Greek numeral	ΡΘ´
Roman numeral	CIX
Binary	11011012
Ternary	110013
Quaternary	12314
Quinary	4145
Senary	3016
Octal	1558
Duodecimal	9112
Hexadecimal	6D16
Vigesimal	5920
Base 36	3136

109 (one hundred [and] nine) is the natural number following 108 and preceding 110.

In mathematics

109 is the 29th prime number. As 29 is itself prime, 109 is the tenth super-prime. The previous prime is 107, making them both twin primes.

109 is a centered triangular number.

There are exactly:

• 109 different families of subsets of a three-element set whose union includes all three elements.
• 109 different loops (invertible but not necessarily associative binary operations with an identity) on six elements.
• 109 squares on an infinite chessboard that can be reached by a knight within three moves.

There are 109 uniform edge-colorings to the 11 regular and semiregular (or Archimedean) tilings.

The decimal expansion of 1/109 can be computed using the alternating series, with [math]\displaystyle{ F(n) }[/math] the [math]\displaystyle{ n^{th} }[/math] Fibonacci number:

[math]\displaystyle{ \frac{1}{109}=\sum_{n=1}^\infty{F(n)\times 10^{-(n+1)}}\times (-1)^{n+1}=0.00917431\dots }[/math]

The decimal expansion of 1/109 has 108 digits, making 109 a full reptend prime in decimal. The last six digits of the 108-digit cycle are 853211, the first six Fibonacci numbers in descending order.

See also

• 109 (disambiguation)