Number reference
19 explained.
19: nineteen, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- nineteen
- Classification
- prime
- Factors
- 1, 19
- Prime factorization
- 19
- Square root
- 4.358899
- Cube root
- 2.668402
- Binary
- 10011
- Octal
- 23
- Hexadecimal
- 13
- Roman numeral
- XIX
- Digit sum
- 10
- Digital root
- 1
What makes 19 notable
- Prime. 19 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
19 in everyday use
Nineteen is the atomic number of potassium. The Metonic cycle, known to Babylonian and Greek astronomers, notes that 235 lunar months fit almost exactly into nineteen solar years, and the Hebrew calendar still adds its leap months on a nineteen-year rhythm. A standard Go board is nineteen lines by nineteen. COVID-19 takes its number from 2019, the year the virus was identified. Golfers call the clubhouse bar the nineteenth hole.
Nineteen is the eighth prime and a centered hexagonal number: a single dot ringed by six and then twelve more, 1 + 6 + 12. It is the largest prime that is a palindrome in Roman numerals, XIX. Nineteen is also a "happy" number: square its digits and add, repeat, and the sequence 82, 68, 100 lands on 1. In the decimal expansion of 1/19 the digits repeat every 18 places, the longest possible cycle for that denominator.
Nearby numbers
How to read this page
Because 19 is prime, the factor list stops at 1 and 19 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 19 in its prime factorisation inherits it from here.
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