The number 8211
8211 is a composite number with 16 divisors. Its prime factorisation is 3 × 7 × 17 × 23. Divisors (16): 1, 3, 7, 17, 21, 23, 51, 69, 119, 161, 357, 391, 483, 1173, 2737, 8211.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8211: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
8211 is composite. Its prime factorisation is
- 3
The divisors add up to 13824; without 8211 itself that is 5613, so 8211 is deficient (5613 is less than 8211). Euler's totient φ(8211) = 4224 numbers up to 8211 share no factor with it.
- 4
The digits of 8211 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 158 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8211 = 3 \times 7 \times 17 \times 23 \]
8211 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 13824 |
| Euler totient φ(n) | 4224 |
| Square | 67420521 |
| Cube | 553589897931 |
| Square root | 90.614568 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 158 |
| Scientific notation | 8.211 × |
8211 in other forms
| Form | Value |
|---|---|
| In words | eight thousand two hundred and eleven |
| Binary (base 2) | 10000000010011 |
| Octal (base 8) | 20023 |
| Hexadecimal (base 16) | 2013 |
| Base 3 | 102021010 |
| As time | 8211 seconds = 2 h 16 min 51 s |
Is 8211 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 | Yes (8211 ÷ 3 = 2737) | 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 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (8211 ÷ 7 = 1173) | 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 3) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8211 a prime number?
No. 8211 = 3 × 7 × 17 × 23, so it is divisible by 3.
What are the factors of 8211?
1, 3, 7, 17, 21, 23, 51, 69, 119, 161, 357, 391, 483, 1173, 2737, 8211.
What is 8211 in binary?
10000000010011 (hexadecimal 2013, octal 20023).
What is the square root of 8211?
About 90.6146.
Is 8211 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 8211?
8211 is a happy number: repeatedly adding the squares of its digits reaches 1.