The number 510
510 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 5 × 17. Divisors (16): 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 510: a Harshad number: divisible by its digit sum 6.
- 2
510 is composite. Its prime factorisation is
- 3
The divisors add up to 1296; without 510 itself that is 786, so 510 is abundant (786 is more than 510). Euler's totient φ(510) = 128 numbers up to 510 share no factor with it.
- 4
The digits of 510 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 510 = 2 \times 3 \times 5 \times 17 \]
510 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 1296 |
| Euler totient φ(n) | 128 |
| Square | 260100 |
| Cube | 132651000 |
| Square root | 22.583180 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 48 |
| Scientific notation | 5.1 × |
510 in other forms
| Form | Value |
|---|---|
| In words | five hundred and ten |
| Roman numerals | DX |
| Binary (base 2) | 111111110 |
| Octal (base 8) | 776 |
| Hexadecimal (base 16) | 1FE |
| Base 3 | 200220 |
| As time | 510 seconds = 8 min 30 s |
Is 510 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (510 ÷ 2 = 255) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (510 ÷ 3 = 170) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (510 ÷ 5 = 102) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (510 ÷ 6 = 85) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (510 ÷ 10 = 51) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 510 a prime number?
No. 510 = 2 × 3 × 5 × 17, so it is divisible by 2.
What are the factors of 510?
1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510.
What is 510 in binary?
111111110 (hexadecimal 1FE, octal 776).
What is the square root of 510?
About 22.5832.
What is 510 in Roman numerals?
DX.
Is 510 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 510?
510 is a Harshad number: divisible by its digit sum 6.