The number 513
513 is a binary palindrome (1000000001). Its prime factorisation is × 19. Divisors (8): 1, 3, 9, 19, 27, 57, 171, 513.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 513: a binary palindrome (1000000001); a Harshad number: divisible by its digit sum 9.
- 2
513 is composite. Its prime factorisation is
- 3
The divisors add up to 800; without 513 itself that is 287, so 513 is deficient (287 is less than 513). Euler's totient φ(513) = 324 numbers up to 513 share no factor with it.
- 4
The digits of 513 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 35 steps to reach 1.
LaTeX source of the formulas on this page
\[ 513 = 3^{3} \times 19 \]513 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 800 |
| Euler totient φ(n) | 324 |
| Square | 263169 |
| Cube | 135005697 |
| Square root | 22.649503 (= 3√57) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 35 |
| Scientific notation | 5.13 × |
513 in other forms
| Form | Value |
|---|---|
| In words | five hundred and thirteen |
| Roman numerals | DXIII |
| Binary (base 2) | 1000000001 |
| Octal (base 8) | 1001 |
| Hexadecimal (base 16) | 201 |
| Base 3 | 201000 |
| As time | 513 seconds = 8 min 33 s |
Is 513 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 | Yes (513 ÷ 3 = 171) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (513 ÷ 9 = 57) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 513 a prime number?
No. 513 = × 19, so it is divisible by 3.
What are the factors of 513?
1, 3, 9, 19, 27, 57, 171, 513.
What is 513 in binary?
1000000001 (hexadecimal 201, octal 1001).
What is the square root of 513?
About 22.6495, exactly 3√57.
What is 513 in Roman numerals?
DXIII.
Is 513 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 513?
513 is a binary palindrome (1000000001); a Harshad number: divisible by its digit sum 9.