The number 111
111 is a palindrome: it reads 111 backwards too. Its prime factorisation is 3 × 37. Divisors (4): 1, 3, 37, 111.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 111: a palindrome: it reads 111 backwards too; a Harshad number: divisible by its digit sum 3; a semiprime: 3 × 37, the product of two primes.
- 2
111 is composite. Its prime factorisation is
- 3
The divisors add up to 152; without 111 itself that is 41, so 111 is deficient (41 is less than 111). Euler's totient φ(111) = 72 numbers up to 111 share no factor with it.
- 4
The digits of 111 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 69 steps to reach 1.
LaTeX source of the formulas on this page
\[ 111 = 3 \times 37 \]
111 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 152 |
| Euler totient φ(n) | 72 |
| Square | 12321 |
| Cube | 1367631 |
| Square root | 10.535654 |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 69 |
| Scientific notation | 1.11 × |
111 in other forms
| Form | Value |
|---|---|
| In words | one hundred and eleven |
| Roman numerals | CXI |
| Binary (base 2) | 1101111 |
| Octal (base 8) | 157 |
| Hexadecimal (base 16) | 6F |
| Base 3 | 11010 |
| As time | 111 seconds = 1 min 51 s |
Is 111 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 (111 ÷ 3 = 37) | 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 7) | 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 1) | 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 111 a prime number?
No. 111 = 3 × 37, so it is divisible by 3.
What are the factors of 111?
1, 3, 37, 111.
What is 111 in binary?
1101111 (hexadecimal 6F, octal 157).
What is the square root of 111?
About 10.5357.
What is 111 in Roman numerals?
CXI.
Is 111 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 111?
111 is a palindrome: it reads 111 backwards too; a Harshad number: divisible by its digit sum 3; a semiprime: 3 × 37, the product of two primes.