The number 18144
18144 is a composite number with 60 divisors. Its prime factorisation is × × 7. Divisors (60): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28 … 18144.
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How to work it out
- 1
What is special about 18144: a Harshad number: divisible by its digit sum 18.
- 2
18144 is composite. Its prime factorisation is
- 3
The divisors add up to 60984; without 18144 itself that is 42840, so 18144 is abundant (42840 is more than 18144). Euler's totient φ(18144) = 5184 numbers up to 18144 share no factor with it.
- 4
The digits of 18144 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 66 steps to reach 1.
LaTeX source of the formulas on this page
\[ 18144 = 2^{5} \times 3^{4} \times 7 \]18144 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 60984 |
| Euler totient φ(n) | 5184 |
| Square | 329204736 |
| Cube | 5973090729984 |
| Square root | 134.699666 (= 36√14) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 66 |
| Scientific notation | 1.8144 × |
18144 in other forms
| Form | Value |
|---|---|
| In words | eighteen thousand one hundred and forty-four |
| Binary (base 2) | 100011011100000 |
| Octal (base 8) | 43340 |
| Hexadecimal (base 16) | 46E0 |
| Base 3 | 220220000 |
| As time | 18144 seconds = 5 h 2 min 24 s |
Is 18144 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (18144 ÷ 2 = 9072) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (18144 ÷ 3 = 6048) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (18144 ÷ 4 = 4536) | 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 (18144 ÷ 6 = 3024) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (18144 ÷ 7 = 2592) | 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 (18144 ÷ 8 = 2268) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (18144 ÷ 9 = 2016) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (18144 ÷ 12 = 1512) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 18144 a prime number?
No. 18144 = × × 7, so it is divisible by 2.
What are the factors of 18144?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 72, 81, 84, 96, 108, 112, 126, 144, 162, 168, 189, 216, 224, 252, 288, 324, 336, 378, 432, 504, 567, 648, 672, 756, 864, 1008, 1134, 1296, 1512, 2016, 2268, 2592, 3024, 4536, 6048, 9072, 18144.
What is 18144 in binary?
100011011100000 (hexadecimal 46E0, octal 43340).
What is the square root of 18144?
About 134.6997, exactly 36√14.
Is 18144 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 18144?
18144 is a Harshad number: divisible by its digit sum 18.