The number 1116
1116 is a composite number with 18 divisors. Its prime factorisation is × × 31. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372 … 1116.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1116: a Harshad number: divisible by its digit sum 9.
- 2
1116 is composite. Its prime factorisation is
- 3
The divisors add up to 2912; without 1116 itself that is 1796, so 1116 is abundant (1796 is more than 1116). Euler's totient φ(1116) = 360 numbers up to 1116 share no factor with it.
- 4
The digits of 1116 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1116 = 2^{2} \times 3^{2} \times 31 \]1116 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 2912 |
| Euler totient φ(n) | 360 |
| Square | 1245456 |
| Cube | 1389928896 |
| Square root | 33.406586 (= 6√31) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 44 |
| Scientific notation | 1.116 × |
1116 in other forms
| Form | Value |
|---|---|
| In words | one thousand one hundred and sixteen |
| Roman numerals | MCXVI |
| Binary (base 2) | 10001011100 |
| Octal (base 8) | 2134 |
| Hexadecimal (base 16) | 45C |
| Base 3 | 1112100 |
| As time | 1116 seconds = 18 min 36 s |
Is 1116 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1116 ÷ 2 = 558) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1116 ÷ 3 = 372) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1116 ÷ 4 = 279) | 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 | Yes (1116 ÷ 6 = 186) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1116 ÷ 9 = 124) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 | Yes (1116 ÷ 12 = 93) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1116 a prime number?
No. 1116 = × × 31, so it is divisible by 2.
What are the factors of 1116?
1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116.
What is 1116 in binary?
10001011100 (hexadecimal 45C, octal 2134).
What is the square root of 1116?
About 33.4066, exactly 6√31.
What is 1116 in Roman numerals?
MCXVI.
Is 1116 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1116?
1116 is a Harshad number: divisible by its digit sum 9.