The number 17955
17955 is a triangular number: 1 + 2 + … + 189 = 17955. Its prime factorisation is × 5 × 7 × 19. Divisors (32): 1, 3, 5, 7, 9, 15, 19, 21, 27, 35, 45, 57, 63, 95, 105, 133 … 17955.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17955: a triangular number: 1 + 2 + … + 189 = 17955; a Harshad number: divisible by its digit sum 27.
- 2
17955 is composite. Its prime factorisation is
- 3
The divisors add up to 38400; without 17955 itself that is 20445, so 17955 is abundant (20445 is more than 17955). Euler's totient φ(17955) = 7776 numbers up to 17955 share no factor with it.
- 4
The digits of 17955 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17955 = 3^{3} \times 5 \times 7 \times 19 \]17955 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 38400 |
| Euler totient φ(n) | 7776 |
| Square | 322382025 |
| Cube | 5788369258875 |
| Square root | 133.996269 (= 3√1995) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 48 |
| Scientific notation | 1.7955 × |
17955 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand nine hundred and fifty-five |
| Binary (base 2) | 100011000100011 |
| Octal (base 8) | 43043 |
| Hexadecimal (base 16) | 4623 |
| Base 3 | 220122000 |
| As time | 17955 seconds = 4 h 59 min 15 s |
Is 17955 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 (17955 ÷ 3 = 5985) | 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 (17955 ÷ 5 = 3591) | 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 | Yes (17955 ÷ 7 = 2565) | 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 (17955 ÷ 9 = 1995) | 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 3) | 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 17955 a prime number?
No. 17955 = × 5 × 7 × 19, so it is divisible by 3.
What are the factors of 17955?
1, 3, 5, 7, 9, 15, 19, 21, 27, 35, 45, 57, 63, 95, 105, 133, 135, 171, 189, 285, 315, 399, 513, 665, 855, 945, 1197, 1995, 2565, 3591, 5985, 17955.
What is 17955 in binary?
100011000100011 (hexadecimal 4623, octal 43043).
What is the square root of 17955?
About 133.9963, exactly 3√1995.
Is 17955 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 17955?
17955 is a triangular number: 1 + 2 + … + 189 = 17955; a Harshad number: divisible by its digit sum 27.