The number 54240
54240 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 113. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 54240.
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How to work it out
- 1
What is special about 54240: a Harshad number: divisible by its digit sum 15.
- 2
54240 is composite. Its prime factorisation is
- 3
The divisors add up to 172368; without 54240 itself that is 118128, so 54240 is abundant (118128 is more than 54240). Euler's totient φ(54240) = 14336 numbers up to 54240 share no factor with it.
- 4
The digits of 54240 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 184 steps to reach 1.
LaTeX source of the formulas on this page
\[ 54240 = 2^{5} \times 3 \times 5 \times 113 \]54240 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 172368 |
| Euler totient φ(n) | 14336 |
| Square | 2941977600 |
| Cube | 159572865024000 |
| Square root | 232.894826 (= 4√3390) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 184 |
| Scientific notation | 5.424 × |
54240 in other forms
| Form | Value |
|---|---|
| In words | fifty-four thousand two hundred and forty |
| Binary (base 2) | 1101001111100000 |
| Octal (base 8) | 151740 |
| Hexadecimal (base 16) | D3E0 |
| Base 3 | 2202101220 |
| As time | 54240 seconds = 15 h 4 min 0 s |
Is 54240 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (54240 ÷ 2 = 27120) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (54240 ÷ 3 = 18080) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (54240 ÷ 4 = 13560) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (54240 ÷ 5 = 10848) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (54240 ÷ 6 = 9040) | 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 (54240 ÷ 8 = 6780) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (54240 ÷ 10 = 5424) | 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 (54240 ÷ 12 = 4520) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 54240 a prime number?
No. 54240 = × 3 × 5 × 113, so it is divisible by 2.
What are the factors of 54240?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 113, 120, 160, 226, 240, 339, 452, 480, 565, 678, 904, 1130, 1356, 1695, 1808, 2260, 2712, 3390, 3616, 4520, 5424, 6780, 9040, 10848, 13560, 18080, 27120, 54240.
What is 54240 in binary?
1101001111100000 (hexadecimal D3E0, octal 151740).
What is the square root of 54240?
About 232.8948, exactly 4√3390.
Is 54240 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 54240?
54240 is a Harshad number: divisible by its digit sum 15.