The number 17280
17280 is a composite number with 64 divisors. Its prime factorisation is × × 5. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27 … 17280.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17280: a Harshad number: divisible by its digit sum 18.
- 2
17280 is composite. Its prime factorisation is
- 3
The divisors add up to 61200; without 17280 itself that is 43920, so 17280 is abundant (43920 is more than 17280). Euler's totient φ(17280) = 4608 numbers up to 17280 share no factor with it.
- 4
The digits of 17280 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 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17280 = 2^{7} \times 3^{3} \times 5 \]17280 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 61200 |
| Euler totient φ(n) | 4608 |
| Square | 298598400 |
| Cube | 5159780352000 |
| Square root | 131.453414 (= 24√30) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 48 |
| Scientific notation | 1.728 × |
17280 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand two hundred and eighty |
| Binary (base 2) | 100001110000000 |
| Octal (base 8) | 41600 |
| Hexadecimal (base 16) | 4380 |
| Base 3 | 212201000 |
| As time | 17280 seconds = 4 h 48 min 0 s |
Is 17280 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17280 ÷ 2 = 8640) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (17280 ÷ 3 = 5760) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17280 ÷ 4 = 4320) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (17280 ÷ 5 = 3456) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (17280 ÷ 6 = 2880) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (17280 ÷ 8 = 2160) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (17280 ÷ 9 = 1920) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (17280 ÷ 10 = 1728) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (17280 ÷ 12 = 1440) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17280 a prime number?
No. 17280 = × × 5, so it is divisible by 2.
What are the factors of 17280?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 128, 135, 144, 160, 180, 192, 216, 240, 270, 288, 320, 360, 384, 432, 480, 540, 576, 640, 720, 864, 960, 1080, 1152, 1440, 1728, 1920, 2160, 2880, 3456, 4320, 5760, 8640, 17280.
What is 17280 in binary?
100001110000000 (hexadecimal 4380, octal 41600).
What is the square root of 17280?
About 131.4534, exactly 24√30.
Is 17280 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 17280?
17280 is a Harshad number: divisible by its digit sum 18.