The number 827
827 is a twin prime (827 and 829 are both prime) and the 144th prime number. Its only divisors are 1 and 827.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 827: a twin prime (827 and 829 are both prime); the 144th prime number.
- 2
827 is prime, so its only factors are 1 and 827. It is the 144th prime; the next prime is 829 and the one before is 823.
- 3
The divisors add up to 828; without 827 itself that is 1, so 827 is deficient (1 is less than 827). Euler's totient φ(827) = 826 numbers up to 827 share no factor with it.
- 4
The digits of 827 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
827 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 828 |
| Euler totient φ(n) | 826 |
| Square | 683929 |
| Cube | 565609283 |
| Square root | 28.757608 |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 41 |
| Scientific notation | 8.27 × |
827 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and twenty-seven |
| Roman numerals | DCCCXXVII |
| Binary (base 2) | 1100111011 |
| Octal (base 8) | 1473 |
| Hexadecimal (base 16) | 33B |
| Base 3 | 1010122 |
| As time | 827 seconds = 13 min 47 s |
Is 827 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 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 1) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 827 a prime number?
Yes. 827 is divisible only by 1 and itself.
What are the factors of 827?
1, 827.
What is 827 in binary?
1100111011 (hexadecimal 33B, octal 1473).
What is the square root of 827?
About 28.7576.
What is 827 in Roman numerals?
DCCCXXVII.
Is 827 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 827?
827 is a twin prime (827 and 829 are both prime); the 144th prime number.