The number 509
509 is the 97th prime number. Its only divisors are 1 and 509.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 509: the 97th prime number.
- 2
509 is prime, so its only factors are 1 and 509. It is the 97th prime; the next prime is 521 and the one before is 503.
- 3
The divisors add up to 510; without 509 itself that is 1, so 509 is deficient (1 is less than 509). Euler's totient φ(509) = 508 numbers up to 509 share no factor with it.
- 4
The digits of 509 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
509 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 510 |
| Euler totient φ(n) | 508 |
| Square | 259081 |
| Cube | 131872229 |
| Square root | 22.561028 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 48 |
| Scientific notation | 5.09 × |
509 in other forms
| Form | Value |
|---|---|
| In words | five hundred and nine |
| Roman numerals | DIX |
| Binary (base 2) | 111111101 |
| Octal (base 8) | 775 |
| Hexadecimal (base 16) | 1FD |
| Base 3 | 200212 |
| As time | 509 seconds = 8 min 29 s |
Is 509 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 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 5) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 509 a prime number?
Yes. 509 is divisible only by 1 and itself.
What are the factors of 509?
1, 509.
What is 509 in binary?
111111101 (hexadecimal 1FD, octal 775).
What is the square root of 509?
About 22.5610.
What is 509 in Roman numerals?
DIX.
Is 509 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 509?
509 is the 97th prime number.