The number 540
540 is a composite number with 24 divisors. Its prime factorisation is × × 5. Divisors (24): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45 … 540.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 540: a Harshad number: divisible by its digit sum 9.
- 2
540 is composite. Its prime factorisation is
- 3
The divisors add up to 1680; without 540 itself that is 1140, so 540 is abundant (1140 is more than 540). Euler's totient φ(540) = 144 numbers up to 540 share no factor with it.
- 4
The digits of 540 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.
LaTeX source of the formulas on this page
\[ 540 = 2^{2} \times 3^{3} \times 5 \]540 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 1680 |
| Euler totient φ(n) | 144 |
| Square | 291600 |
| Cube | 157464000 |
| Square root | 23.237900 (= 6√15) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 43 |
| Scientific notation | 5.4 × |
540 in other forms
| Form | Value |
|---|---|
| In words | five hundred and forty |
| Roman numerals | DXL |
| Binary (base 2) | 1000011100 |
| Octal (base 8) | 1034 |
| Hexadecimal (base 16) | 21C |
| Base 3 | 202000 |
| As time | 540 seconds = 9 min 0 s |
Is 540 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (540 ÷ 2 = 270) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (540 ÷ 3 = 180) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (540 ÷ 4 = 135) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (540 ÷ 5 = 108) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (540 ÷ 6 = 90) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (540 ÷ 9 = 60) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (540 ÷ 10 = 54) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (540 ÷ 12 = 45) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 540 a prime number?
No. 540 = × × 5, so it is divisible by 2.
What are the factors of 540?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.
What is 540 in binary?
1000011100 (hexadecimal 21C, octal 1034).
What is the square root of 540?
About 23.2379, exactly 6√15.
What is 540 in Roman numerals?
DXL.
Is 540 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 540?
540 is a Harshad number: divisible by its digit sum 9.