The number 27744
27744 is a composite number with 36 divisors. Its prime factorisation is × 3 × . Divisors (36): 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 68, 96 … 27744.
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How to work it out
- 1
What is special about 27744: a Harshad number: divisible by its digit sum 24.
- 2
27744 is composite. Its prime factorisation is
- 3
The divisors add up to 77364; without 27744 itself that is 49620, so 27744 is abundant (49620 is more than 27744). Euler's totient φ(27744) = 8704 numbers up to 27744 share no factor with it.
- 4
The digits of 27744 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 33 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27744 = 2^{5} \times 3 \times 17^{2} \]27744 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 77364 |
| Euler totient φ(n) | 8704 |
| Square | 769729536 |
| Cube | 21355376246784 |
| Square root | 166.565303 (= 68√6) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 33 |
| Scientific notation | 2.7744 × |
27744 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand seven hundred and forty-four |
| Binary (base 2) | 110110001100000 |
| Octal (base 8) | 66140 |
| Hexadecimal (base 16) | 6C60 |
| Base 3 | 1102001120 |
| As time | 27744 seconds = 7 h 42 min 24 s |
Is 27744 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27744 ÷ 2 = 13872) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27744 ÷ 3 = 9248) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27744 ÷ 4 = 6936) | 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 (27744 ÷ 6 = 4624) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (27744 ÷ 8 = 3468) | 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 | 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 (27744 ÷ 12 = 2312) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27744 a prime number?
No. 27744 = × 3 × , so it is divisible by 2.
What are the factors of 27744?
1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 68, 96, 102, 136, 204, 272, 289, 408, 544, 578, 816, 867, 1156, 1632, 1734, 2312, 3468, 4624, 6936, 9248, 13872, 27744.
What is 27744 in binary?
110110001100000 (hexadecimal 6C60, octal 66140).
What is the square root of 27744?
About 166.5653, exactly 68√6.
Is 27744 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 27744?
27744 is a Harshad number: divisible by its digit sum 24.