The number 2211
2211 is a triangular number: 1 + 2 + … + 66 = 2211. Its prime factorisation is 3 × 11 × 67. Divisors (8): 1, 3, 11, 33, 67, 201, 737, 2211.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2211: a triangular number: 1 + 2 + … + 66 = 2211; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
2211 is composite. Its prime factorisation is
- 3
The divisors add up to 3264; without 2211 itself that is 1053, so 2211 is deficient (1053 is less than 2211). Euler's totient φ(2211) = 1320 numbers up to 2211 share no factor with it.
- 4
The digits of 2211 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2211 = 3 \times 11 \times 67 \]
2211 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 3264 |
| Euler totient φ(n) | 1320 |
| Square | 4888521 |
| Cube | 10808519931 |
| Square root | 47.021272 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 94 |
| Scientific notation | 2.211 × |
2211 in other forms
| Form | Value |
|---|---|
| In words | two thousand two hundred and eleven |
| Roman numerals | MMCCXI |
| Binary (base 2) | 100010100011 |
| Octal (base 8) | 4243 |
| Hexadecimal (base 16) | 8A3 |
| Base 3 | 10000220 |
| As time | 2211 seconds = 36 min 51 s |
Is 2211 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 (2211 ÷ 3 = 737) | 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 | No (remainder 6) | 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 6) | 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 | Yes (2211 ÷ 11 = 201) | 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 2211 a prime number?
No. 2211 = 3 × 11 × 67, so it is divisible by 3.
What are the factors of 2211?
1, 3, 11, 33, 67, 201, 737, 2211.
What is 2211 in binary?
100010100011 (hexadecimal 8A3, octal 4243).
What is the square root of 2211?
About 47.0213.
What is 2211 in Roman numerals?
MMCCXI.
Is 2211 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 2211?
2211 is a triangular number: 1 + 2 + … + 66 = 2211; a happy number: repeatedly adding the squares of its digits reaches 1.