The number 27648
27648 is a composite number with 44 divisors. Its prime factorisation is × . Divisors (44): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 27648.
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How to work it out
- 1
What is special about 27648: a Harshad number: divisible by its digit sum 27.
- 2
27648 is composite. Its prime factorisation is
- 3
The divisors add up to 81880; without 27648 itself that is 54232, so 27648 is abundant (54232 is more than 27648). Euler's totient φ(27648) = 9216 numbers up to 27648 share no factor with it.
- 4
The digits of 27648 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 121 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27648 = 2^{10} \times 3^{3} \]27648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 44 |
| Sum of divisors | 81880 |
| Euler totient φ(n) | 9216 |
| Square | 764411904 |
| Cube | 21134460321792 |
| Square root | 166.276878 (= 96√3) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 121 |
| Scientific notation | 2.7648 × |
27648 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand six hundred and forty-eight |
| Binary (base 2) | 110110000000000 |
| Octal (base 8) | 66000 |
| Hexadecimal (base 16) | 6C00 |
| Base 3 | 1101221000 |
| As time | 27648 seconds = 7 h 40 min 48 s |
Is 27648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27648 ÷ 2 = 13824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27648 ÷ 3 = 9216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27648 ÷ 4 = 6912) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (27648 ÷ 6 = 4608) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (27648 ÷ 8 = 3456) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27648 ÷ 9 = 3072) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 (27648 ÷ 12 = 2304) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27648 a prime number?
No. 27648 = × , so it is divisible by 2.
What are the factors of 27648?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1024, 1152, 1536, 1728, 2304, 3072, 3456, 4608, 6912, 9216, 13824, 27648.
What is 27648 in binary?
110110000000000 (hexadecimal 6C00, octal 66000).
What is the square root of 27648?
About 166.2769, exactly 96√3.
Is 27648 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 27648?
27648 is a Harshad number: divisible by its digit sum 27.