The number 27360
27360 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 19. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24 … 27360.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27360: a Harshad number: divisible by its digit sum 18.
- 2
27360 is composite. Its prime factorisation is
- 3
The divisors add up to 98280; without 27360 itself that is 70920, so 27360 is abundant (70920 is more than 27360). Euler's totient φ(27360) = 6912 numbers up to 27360 share no factor with it.
- 4
The digits of 27360 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 59 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27360 = 2^{5} \times 3^{2} \times 5 \times 19 \]27360 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 98280 |
| Euler totient φ(n) | 6912 |
| Square | 748569600 |
| Cube | 20480864256000 |
| Square root | 165.408585 (= 12√190) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 59 |
| Scientific notation | 2.736 × |
27360 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand three hundred and sixty |
| Binary (base 2) | 110101011100000 |
| Octal (base 8) | 65340 |
| Hexadecimal (base 16) | 6AE0 |
| Base 3 | 1101112100 |
| As time | 27360 seconds = 7 h 36 min 0 s |
Is 27360 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27360 ÷ 2 = 13680) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27360 ÷ 3 = 9120) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27360 ÷ 4 = 6840) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27360 ÷ 5 = 5472) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27360 ÷ 6 = 4560) | 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 (27360 ÷ 8 = 3420) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27360 ÷ 9 = 3040) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (27360 ÷ 10 = 2736) | 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 | Yes (27360 ÷ 12 = 2280) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27360 a prime number?
No. 27360 = × × 5 × 19, so it is divisible by 2.
What are the factors of 27360?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 30, 32, 36, 38, 40, 45, 48, 57, 60, 72, 76, 80, 90, 95, 96, 114, 120, 144, 152, 160, 171, 180, 190, 228, 240, 285, 288, 304, 342, 360, 380, 456, 480, 570, 608, 684, 720, 760, 855, 912, 1140, 1368, 1440, 1520, 1710, 1824, 2280, 2736, 3040, 3420, 4560, 5472, 6840, 9120, 13680, 27360.
What is 27360 in binary?
110101011100000 (hexadecimal 6AE0, octal 65340).
What is the square root of 27360?
About 165.4086, exactly 12√190.
Is 27360 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 27360?
27360 is a Harshad number: divisible by its digit sum 18.