The number 19
19 is a twin prime (17 and 19 are both prime) and the 8th prime number. Its only divisors are 1 and 19.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 19: a twin prime (17 and 19 are both prime); the 8th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
19 is prime, so its only factors are 1 and 19. It is the 8th prime; the next prime is 23 and the one before is 17.
- 3
The divisors add up to 20; without 19 itself that is 1, so 19 is deficient (1 is less than 19). Euler's totient φ(19) = 18 numbers up to 19 share no factor with it.
- 4
The digits of 19 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 20 steps to reach 1.
19 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 20 |
| Euler totient φ(n) | 18 |
| Square | 361 |
| Cube | 6859 |
| Square root | 4.358899 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 20 |
| Scientific notation | 1.9 × |
19 in other forms
| Form | Value |
|---|---|
| In words | nineteen |
| Roman numerals | XIX |
| Binary (base 2) | 10011 |
| Octal (base 8) | 23 |
| Hexadecimal (base 16) | 13 |
| Base 3 | 201 |
| As time | 19 seconds |
Is 19 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 19 a prime number?
Yes. 19 is divisible only by 1 and itself.
What are the factors of 19?
1, 19.
What is 19 in binary?
10011 (hexadecimal 13, octal 23).
What is the square root of 19?
About 4.3589.
What is 19 in Roman numerals?
XIX.
Is 19 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 19?
19 is a twin prime (17 and 19 are both prime); the 8th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.