The number 810
810 is a composite number with 20 divisors. Its prime factorisation is 2 × × 5. Divisors (20): 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135 … 810.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 810: a Harshad number: divisible by its digit sum 9.
- 2
810 is composite. Its prime factorisation is
- 3
The divisors add up to 2178; without 810 itself that is 1368, so 810 is abundant (1368 is more than 810). Euler's totient φ(810) = 216 numbers up to 810 share no factor with it.
- 4
The digits of 810 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 28 steps to reach 1.
LaTeX source of the formulas on this page
\[ 810 = 2 \times 3^{4} \times 5 \]810 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 2178 |
| Euler totient φ(n) | 216 |
| Square | 656100 |
| Cube | 531441000 |
| Square root | 28.460499 (= 9√10) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 28 |
| Scientific notation | 8.1 × |
810 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and ten |
| Roman numerals | DCCCX |
| Binary (base 2) | 1100101010 |
| Octal (base 8) | 1452 |
| Hexadecimal (base 16) | 32A |
| Base 3 | 1010000 |
| As time | 810 seconds = 13 min 30 s |
Is 810 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (810 ÷ 2 = 405) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (810 ÷ 3 = 270) | 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 (810 ÷ 5 = 162) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (810 ÷ 6 = 135) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (810 ÷ 9 = 90) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (810 ÷ 10 = 81) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 810 a prime number?
No. 810 = 2 × × 5, so it is divisible by 2.
What are the factors of 810?
1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810.
What is 810 in binary?
1100101010 (hexadecimal 32A, octal 1452).
What is the square root of 810?
About 28.4605, exactly 9√10.
What is 810 in Roman numerals?
DCCCX.
Is 810 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 810?
810 is a Harshad number: divisible by its digit sum 9.