The number 821
821 is a twin prime (821 and 823 are both prime) and the 142nd prime number. Its only divisors are 1 and 821.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 821: a twin prime (821 and 823 are both prime); the 142nd prime number.
- 2
821 is prime, so its only factors are 1 and 821. It is the 142nd prime; the next prime is 823 and the one before is 811.
- 3
The divisors add up to 822; without 821 itself that is 1, so 821 is deficient (1 is less than 821). Euler's totient φ(821) = 820 numbers up to 821 share no factor with it.
- 4
The digits of 821 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 28 steps to reach 1.
821 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 822 |
| Euler totient φ(n) | 820 |
| Square | 674041 |
| Cube | 553387661 |
| Square root | 28.653098 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 28 |
| Scientific notation | 8.21 × |
821 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and twenty-one |
| Roman numerals | DCCCXXI |
| Binary (base 2) | 1100110101 |
| Octal (base 8) | 1465 |
| Hexadecimal (base 16) | 335 |
| Base 3 | 1010102 |
| As time | 821 seconds = 13 min 41 s |
Is 821 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 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 821 a prime number?
Yes. 821 is divisible only by 1 and itself.
What are the factors of 821?
1, 821.
What is 821 in binary?
1100110101 (hexadecimal 335, octal 1465).
What is the square root of 821?
About 28.6531.
What is 821 in Roman numerals?
DCCCXXI.
Is 821 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 821?
821 is a twin prime (821 and 823 are both prime); the 142nd prime number.