The number 2011
2011 is the 305th prime number. Its only divisors are 1 and 2011.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2011: the 305th prime number.
- 2
2011 is prime, so its only factors are 1 and 2011. It is the 305th prime; the next prime is 2017 and the one before is 2003.
- 3
The divisors add up to 2012; without 2011 itself that is 1, so 2011 is deficient (1 is less than 2011). Euler's totient φ(2011) = 2010 numbers up to 2011 share no factor with it.
- 4
The digits of 2011 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
2011 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 2012 |
| Euler totient φ(n) | 2010 |
| Square | 4044121 |
| Cube | 8132727331 |
| Square root | 44.844175 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 42 |
| Scientific notation | 2.011 × |
2011 in other forms
| Form | Value |
|---|---|
| In words | two thousand and eleven |
| Roman numerals | MMXI |
| Binary (base 2) | 11111011011 |
| Octal (base 8) | 3733 |
| Hexadecimal (base 16) | 7DB |
| Base 3 | 2202111 |
| As time | 2011 seconds = 33 min 31 s |
Is 2011 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 1) | 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 1) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2011 a prime number?
Yes. 2011 is divisible only by 1 and itself.
What are the factors of 2011?
1, 2011.
What is 2011 in binary?
11111011011 (hexadecimal 7DB, octal 3733).
What is the square root of 2011?
About 44.8442.
What is 2011 in Roman numerals?
MMXI.
Is 2011 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 2011?
2011 is the 305th prime number.