The number 27824
27824 is a composite number with 20 divisors. Its prime factorisation is × 37 × 47. Divisors (20): 1, 2, 4, 8, 16, 37, 47, 74, 94, 148, 188, 296, 376, 592, 752, 1739 … 27824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
27824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
27824 is composite. Its prime factorisation is
- 3
The divisors add up to 56544; without 27824 itself that is 28720, so 27824 is abundant (28720 is more than 27824). Euler's totient φ(27824) = 13248 numbers up to 27824 share no factor with it.
- 4
The digits of 27824 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 59 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27824 = 2^{4} \times 37 \times 47 \]27824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 56544 |
| Euler totient φ(n) | 13248 |
| Square | 774174976 |
| Cube | 21540644532224 |
| Square root | 166.805276 (= 4√1739) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 59 |
| Scientific notation | 2.7824 × |
27824 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand eight hundred and twenty-four |
| Binary (base 2) | 110110010110000 |
| Octal (base 8) | 66260 |
| Hexadecimal (base 16) | 6CB0 |
| Base 3 | 1102011112 |
| As time | 27824 seconds = 7 h 43 min 44 s |
Is 27824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27824 ÷ 2 = 13912) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27824 ÷ 4 = 6956) | 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 | No (remainder 2) | 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 (27824 ÷ 8 = 3478) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27824 a prime number?
No. 27824 = × 37 × 47, so it is divisible by 2.
What are the factors of 27824?
1, 2, 4, 8, 16, 37, 47, 74, 94, 148, 188, 296, 376, 592, 752, 1739, 3478, 6956, 13912, 27824.
What is 27824 in binary?
110110010110000 (hexadecimal 6CB0, octal 66260).
What is the square root of 27824?
About 166.8053, exactly 4√1739.
Is 27824 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 27824?
It is a composite number with 20 divisors.