The number 823
823 is a twin prime (821 and 823 are both prime) and the 143rd prime number. Its only divisors are 1 and 823.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 823: a twin prime (821 and 823 are both prime); the 143rd prime number.
- 2
823 is prime, so its only factors are 1 and 823. It is the 143rd prime; the next prime is 827 and the one before is 821.
- 3
The divisors add up to 824; without 823 itself that is 1, so 823 is deficient (1 is less than 823). Euler's totient φ(823) = 822 numbers up to 823 share no factor with it.
- 4
The digits of 823 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 134 steps to reach 1.
823 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 824 |
| Euler totient φ(n) | 822 |
| Square | 677329 |
| Cube | 557441767 |
| Square root | 28.687977 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 134 |
| Scientific notation | 8.23 × |
823 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and twenty-three |
| Roman numerals | DCCCXXIII |
| Binary (base 2) | 1100110111 |
| Octal (base 8) | 1467 |
| Hexadecimal (base 16) | 337 |
| Base 3 | 1010111 |
| As time | 823 seconds = 13 min 43 s |
Is 823 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 3) | 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 4) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 9) | 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 823 a prime number?
Yes. 823 is divisible only by 1 and itself.
What are the factors of 823?
1, 823.
What is 823 in binary?
1100110111 (hexadecimal 337, octal 1467).
What is the square root of 823?
About 28.6880.
What is 823 in Roman numerals?
DCCCXXIII.
Is 823 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 823?
823 is a twin prime (821 and 823 are both prime); the 143rd prime number.