The number 17880
17880 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 149. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 17880.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17880: a Harshad number: divisible by its digit sum 24.
- 2
17880 is composite. Its prime factorisation is
- 3
The divisors add up to 54000; without 17880 itself that is 36120, so 17880 is abundant (36120 is more than 17880). Euler's totient φ(17880) = 4736 numbers up to 17880 share no factor with it.
- 4
The digits of 17880 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17880 = 2^{3} \times 3 \times 5 \times 149 \]17880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 54000 |
| Euler totient φ(n) | 4736 |
| Square | 319694400 |
| Cube | 5716135872000 |
| Square root | 133.716117 (= 2√4470) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 48 |
| Scientific notation | 1.788 × |
17880 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand eight hundred and eighty |
| Binary (base 2) | 100010111011000 |
| Octal (base 8) | 42730 |
| Hexadecimal (base 16) | 45D8 |
| Base 3 | 220112020 |
| As time | 17880 seconds = 4 h 58 min 0 s |
Is 17880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17880 ÷ 2 = 8940) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (17880 ÷ 3 = 5960) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17880 ÷ 4 = 4470) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (17880 ÷ 5 = 3576) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (17880 ÷ 6 = 2980) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (17880 ÷ 8 = 2235) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (17880 ÷ 10 = 1788) | 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 (17880 ÷ 12 = 1490) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17880 a prime number?
No. 17880 = × 3 × 5 × 149, so it is divisible by 2.
What are the factors of 17880?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 149, 298, 447, 596, 745, 894, 1192, 1490, 1788, 2235, 2980, 3576, 4470, 5960, 8940, 17880.
What is 17880 in binary?
100010111011000 (hexadecimal 45D8, octal 42730).
What is the square root of 17880?
About 133.7161, exactly 2√4470.
Is 17880 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 17880?
17880 is a Harshad number: divisible by its digit sum 24.