The number 822
822 is a composite number with 8 divisors. Its prime factorisation is 2 × 3 × 137. Divisors (8): 1, 2, 3, 6, 137, 274, 411, 822.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
822 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
822 is composite. Its prime factorisation is
- 3
The divisors add up to 1656; without 822 itself that is 834, so 822 is abundant (834 is more than 822). Euler's totient φ(822) = 272 numbers up to 822 share no factor with it.
- 4
The digits of 822 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 134 steps to reach 1.
LaTeX source of the formulas on this page
\[ 822 = 2 \times 3 \times 137 \]
822 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1656 |
| Euler totient φ(n) | 272 |
| Square | 675684 |
| Cube | 555412248 |
| Square root | 28.670542 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 134 |
| Scientific notation | 8.22 × |
822 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and twenty-two |
| Roman numerals | DCCCXXII |
| Binary (base 2) | 1100110110 |
| Octal (base 8) | 1466 |
| Hexadecimal (base 16) | 336 |
| Base 3 | 1010110 |
| As time | 822 seconds = 13 min 42 s |
Is 822 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (822 ÷ 2 = 411) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (822 ÷ 3 = 274) | 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 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (822 ÷ 6 = 137) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | 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 822 a prime number?
No. 822 = 2 × 3 × 137, so it is divisible by 2.
What are the factors of 822?
1, 2, 3, 6, 137, 274, 411, 822.
What is 822 in binary?
1100110110 (hexadecimal 336, octal 1466).
What is the square root of 822?
About 28.6705.
What is 822 in Roman numerals?
DCCCXXII.
Is 822 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 822?
It is a composite number with 8 divisors.