The number 11
11 is a palindromic prime: it reads the same backwards and is prime, a twin prime (11 and 13 are both prime) and the 5th prime number. Its only divisors are 1 and 11.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 11: a palindromic prime: it reads the same backwards and is prime; a twin prime (11 and 13 are both prime); the 5th prime number; a palindrome: it reads 11 backwards too.
- 2
11 is prime, so its only factors are 1 and 11. It is the 5th prime; the next prime is 13 and the one before is 7.
- 3
The divisors add up to 12; without 11 itself that is 1, so 11 is deficient (1 is less than 11). Euler's totient φ(11) = 10 numbers up to 11 share no factor with it.
- 4
The digits of 11 add up to 2, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 14 steps to reach 1.
11 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 12 |
| Euler totient φ(n) | 10 |
| Square | 121 |
| Cube | 1331 |
| Square root | 3.316625 |
| Digit sum / digital root | 2 / 2 |
| Collatz steps to 1 | 14 |
| Scientific notation | 1.1 × |
11 in other forms
| Form | Value |
|---|---|
| In words | eleven |
| Roman numerals | XI |
| Binary (base 2) | 1011 |
| Octal (base 8) | 13 |
| Hexadecimal (base 16) | B |
| Base 3 | 102 |
| As time | 11 seconds |
Is 11 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 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 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 | Yes (11 ÷ 11 = 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 11 a prime number?
Yes. 11 is divisible only by 1 and itself.
What are the factors of 11?
1, 11.
What is 11 in binary?
1011 (hexadecimal B, octal 13).
What is the square root of 11?
About 3.3166.
What is 11 in Roman numerals?
XI.
Is 11 divisible by 3?
No. Its digits add up to 2, which is not a multiple of 3.
What is special about the number 11?
11 is a palindromic prime: it reads the same backwards and is prime; a twin prime (11 and 13 are both prime); the 5th prime number; a palindrome: it reads 11 backwards too.