Number reference
109 explained.
109: one hundred nine, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred nine
- Classification
- prime
- Factors
- 1, 109
- Prime factorization
- 109
- Square root
- 10.440307
- Cube root
- 4.776856
- Binary
- 1101101
- Octal
- 155
- Hexadecimal
- 6D
- Roman numeral
- CIX
- Digit sum
- 10
- Digital root
- 1
What makes 109 notable
- Prime. 109 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
109 in everyday use
One hundred nine is the atomic number of meitnerium, named for the physicist Lise Meitner, who co-discovered nuclear fission. In Tokyo the number is a landmark: the Shibuya 109 department store, opened in 1979, takes its name from a pun on its parent company Tokyu, since "to" and "kyu" can be read as ten and nine in Japanese. The building became a centre of youth fashion, and its cylindrical tower is one of the most photographed sights at the Shibuya crossing.
Mathematically, 109 is prime and pairs with 107 as twin primes. It can be written as the sum of two squares, 10² + 3², and it is a full-reptend prime: the decimal expansion of 1/109 repeats with the longest possible period of 108 digits before starting over. Its reversal, 901, factors as 17 × 53, so unlike some of its neighbours it is not an emirp.
Nearby numbers
How to read this page
Because 109 is prime, the factor list stops at 1 and 109 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 109 in its prime factorisation inherits it from here.
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