The number 1105
1105 is a binary palindrome (10001010001). Its prime factorisation is 5 × 13 × 17. Divisors (8): 1, 5, 13, 17, 65, 85, 221, 1105.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1105: a binary palindrome (10001010001).
- 2
1105 is composite. Its prime factorisation is
- 3
The divisors add up to 1512; without 1105 itself that is 407, so 1105 is deficient (407 is less than 1105). Euler's totient φ(1105) = 768 numbers up to 1105 share no factor with it.
- 4
The digits of 1105 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1105 = 5 \times 13 \times 17 \]
1105 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1512 |
| Euler totient φ(n) | 768 |
| Square | 1221025 |
| Cube | 1349232625 |
| Square root | 33.241540 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 93 |
| Scientific notation | 1.105 × |
1105 in other forms
| Form | Value |
|---|---|
| In words | one thousand one hundred and five |
| Roman numerals | MCV |
| Binary (base 2) | 10001010001 |
| Octal (base 8) | 2121 |
| Hexadecimal (base 16) | 451 |
| Base 3 | 1111221 |
| As time | 1105 seconds = 18 min 25 s |
Is 1105 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 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1105 ÷ 5 = 221) | 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 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | 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 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1105 a prime number?
No. 1105 = 5 × 13 × 17, so it is divisible by 5.
What are the factors of 1105?
1, 5, 13, 17, 65, 85, 221, 1105.
What is 1105 in binary?
10001010001 (hexadecimal 451, octal 2121).
What is the square root of 1105?
About 33.2415.
What is 1105 in Roman numerals?
MCV.
Is 1105 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 1105?
1105 is a binary palindrome (10001010001).