The number 27540
27540 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 17. Divisors (60): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 27, 30, 34 … 27540.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27540: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
27540 is composite. Its prime factorisation is
- 3
The divisors add up to 91476; without 27540 itself that is 63936, so 27540 is abundant (63936 is more than 27540). Euler's totient φ(27540) = 6912 numbers up to 27540 share no factor with it.
- 4
The digits of 27540 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
\[ 27540 = 2^{2} \times 3^{4} \times 5 \times 17 \]27540 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 91476 |
| Euler totient φ(n) | 6912 |
| Square | 758451600 |
| Cube | 20887757064000 |
| Square root | 165.951800 (= 18√85) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 59 |
| Scientific notation | 2.754 × |
27540 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand five hundred and forty |
| Binary (base 2) | 110101110010100 |
| Octal (base 8) | 65624 |
| Hexadecimal (base 16) | 6B94 |
| Base 3 | 1101210000 |
| As time | 27540 seconds = 7 h 39 min 0 s |
Is 27540 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27540 ÷ 2 = 13770) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27540 ÷ 3 = 9180) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27540 ÷ 4 = 6885) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27540 ÷ 5 = 5508) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27540 ÷ 6 = 4590) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27540 ÷ 9 = 3060) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (27540 ÷ 10 = 2754) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27540 ÷ 12 = 2295) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27540 a prime number?
No. 27540 = × × 5 × 17, so it is divisible by 2.
What are the factors of 27540?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 27, 30, 34, 36, 45, 51, 54, 60, 68, 81, 85, 90, 102, 108, 135, 153, 162, 170, 180, 204, 255, 270, 306, 324, 340, 405, 459, 510, 540, 612, 765, 810, 918, 1020, 1377, 1530, 1620, 1836, 2295, 2754, 3060, 4590, 5508, 6885, 9180, 13770, 27540.
What is 27540 in binary?
110101110010100 (hexadecimal 6B94, octal 65624).
What is the square root of 27540?
About 165.9518, exactly 18√85.
Is 27540 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 27540?
27540 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.