The number 54000
54000 is a composite number with 80 divisors. Its prime factorisation is × × . Divisors (80): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25 … 54000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 54000: a Harshad number: divisible by its digit sum 9.
- 2
54000 is composite. Its prime factorisation is
- 3
The divisors add up to 193440; without 54000 itself that is 139440, so 54000 is abundant (139440 is more than 54000). Euler's totient φ(54000) = 14400 numbers up to 54000 share no factor with it.
- 4
The digits of 54000 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 140 steps to reach 1.
LaTeX source of the formulas on this page
\[ 54000 = 2^{4} \times 3^{3} \times 5^{3} \]54000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 193440 |
| Euler totient φ(n) | 14400 |
| Square | 2916000000 |
| Cube | 157464000000000 |
| Square root | 232.379001 (= 60√15) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 140 |
| Scientific notation | 5.4 × |
54000 in other forms
| Form | Value |
|---|---|
| In words | fifty-four thousand |
| Binary (base 2) | 1101001011110000 |
| Octal (base 8) | 151360 |
| Hexadecimal (base 16) | D2F0 |
| Base 3 | 2202002000 |
| As time | 54000 seconds = 15 h 0 min 0 s |
Is 54000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (54000 ÷ 2 = 27000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (54000 ÷ 3 = 18000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (54000 ÷ 4 = 13500) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (54000 ÷ 5 = 10800) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (54000 ÷ 6 = 9000) | 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 (54000 ÷ 8 = 6750) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (54000 ÷ 9 = 6000) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (54000 ÷ 10 = 5400) | 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 (54000 ÷ 12 = 4500) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 54000 a prime number?
No. 54000 = × × , so it is divisible by 2.
What are the factors of 54000?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 100, 108, 120, 125, 135, 144, 150, 180, 200, 216, 225, 240, 250, 270, 300, 360, 375, 400, 432, 450, 500, 540, 600, 675, 720, 750, 900, 1000, 1080, 1125, 1200, 1350, 1500, 1800, 2000, 2160, 2250, 2700, 3000, 3375, 3600, 4500, 5400, 6000, 6750, 9000, 10800, 13500, 18000, 27000, 54000.
What is 54000 in binary?
1101001011110000 (hexadecimal D2F0, octal 151360).
What is the square root of 54000?
About 232.3790, exactly 60√15.
Is 54000 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 54000?
54000 is a Harshad number: divisible by its digit sum 9.