The number 1755
1755 is a binary palindrome (11011011011). Its prime factorisation is × 5 × 13. Divisors (16): 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1755: a binary palindrome (11011011011); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1755 is composite. Its prime factorisation is
- 3
The divisors add up to 3360; without 1755 itself that is 1605, so 1755 is deficient (1605 is less than 1755). Euler's totient φ(1755) = 864 numbers up to 1755 share no factor with it.
- 4
The digits of 1755 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1755 = 3^{3} \times 5 \times 13 \]1755 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 3360 |
| Euler totient φ(n) | 864 |
| Square | 3080025 |
| Cube | 5405443875 |
| Square root | 41.892720 (= 3√195) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.755 × |
1755 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and fifty-five |
| Roman numerals | MDCCLV |
| Binary (base 2) | 11011011011 |
| Octal (base 8) | 3333 |
| Hexadecimal (base 16) | 6DB |
| Base 3 | 2102000 |
| As time | 1755 seconds = 29 min 15 s |
Is 1755 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 (1755 ÷ 3 = 585) | 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 | Yes (1755 ÷ 5 = 351) | 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 5) | 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 (1755 ÷ 9 = 195) | 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 6) | 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 1755 a prime number?
No. 1755 = × 5 × 13, so it is divisible by 3.
What are the factors of 1755?
1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755.
What is 1755 in binary?
11011011011 (hexadecimal 6DB, octal 3333).
What is the square root of 1755?
About 41.8927, exactly 3√195.
What is 1755 in Roman numerals?
MDCCLV.
Is 1755 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1755?
1755 is a binary palindrome (11011011011); a happy number: repeatedly adding the squares of its digits reaches 1.