The number 54144
54144 is a composite number with 48 divisors. Its prime factorisation is × × 47. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 47, 48, 64 … 54144.
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How to work it out
- 1
What is special about 54144: a Harshad number: divisible by its digit sum 18.
- 2
54144 is composite. Its prime factorisation is
- 3
The divisors add up to 159120; without 54144 itself that is 104976, so 54144 is abundant (104976 is more than 54144). Euler's totient φ(54144) = 17664 numbers up to 54144 share no factor with it.
- 4
The digits of 54144 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 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 54144 = 2^{7} \times 3^{2} \times 47 \]54144 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 159120 |
| Euler totient φ(n) | 17664 |
| Square | 2931572736 |
| Cube | 158727074217984 |
| Square root | 232.688633 (= 24√94) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 39 |
| Scientific notation | 5.4144 × |
54144 in other forms
| Form | Value |
|---|---|
| In words | fifty-four thousand one hundred and forty-four |
| Binary (base 2) | 1101001110000000 |
| Octal (base 8) | 151600 |
| Hexadecimal (base 16) | D380 |
| Base 3 | 2202021100 |
| As time | 54144 seconds = 15 h 2 min 24 s |
Is 54144 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (54144 ÷ 2 = 27072) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (54144 ÷ 3 = 18048) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (54144 ÷ 4 = 13536) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (54144 ÷ 6 = 9024) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (54144 ÷ 8 = 6768) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (54144 ÷ 9 = 6016) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (54144 ÷ 12 = 4512) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 54144 a prime number?
No. 54144 = × × 47, so it is divisible by 2.
What are the factors of 54144?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 47, 48, 64, 72, 94, 96, 128, 141, 144, 188, 192, 282, 288, 376, 384, 423, 564, 576, 752, 846, 1128, 1152, 1504, 1692, 2256, 3008, 3384, 4512, 6016, 6768, 9024, 13536, 18048, 27072, 54144.
What is 54144 in binary?
1101001110000000 (hexadecimal D380, octal 151600).
What is the square root of 54144?
About 232.6886, exactly 24√94.
Is 54144 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 54144?
54144 is a Harshad number: divisible by its digit sum 18.