The number 1107
1107 is a composite number with 8 divisors. Its prime factorisation is × 41. Divisors (8): 1, 3, 9, 27, 41, 123, 369, 1107.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1107: a Harshad number: divisible by its digit sum 9.
- 2
1107 is composite. Its prime factorisation is
- 3
The divisors add up to 1680; without 1107 itself that is 573, so 1107 is deficient (573 is less than 1107). Euler's totient φ(1107) = 720 numbers up to 1107 share no factor with it.
- 4
The digits of 1107 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 137 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1107 = 3^{3} \times 41 \]1107 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1680 |
| Euler totient φ(n) | 720 |
| Square | 1225449 |
| Cube | 1356572043 |
| Square root | 33.271610 (= 3√123) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 137 |
| Scientific notation | 1.107 × |
1107 in other forms
| Form | Value |
|---|---|
| In words | one thousand one hundred and seven |
| Roman numerals | MCVII |
| Binary (base 2) | 10001010011 |
| Octal (base 8) | 2123 |
| Hexadecimal (base 16) | 453 |
| Base 3 | 1112000 |
| As time | 1107 seconds = 18 min 27 s |
Is 1107 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 (1107 ÷ 3 = 369) | 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 2) | 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 1) | 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 | Yes (1107 ÷ 9 = 123) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 1107 a prime number?
No. 1107 = × 41, so it is divisible by 3.
What are the factors of 1107?
1, 3, 9, 27, 41, 123, 369, 1107.
What is 1107 in binary?
10001010011 (hexadecimal 453, octal 2123).
What is the square root of 1107?
About 33.2716, exactly 3√123.
What is 1107 in Roman numerals?
MCVII.
Is 1107 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1107?
1107 is a Harshad number: divisible by its digit sum 9.