The number 27968
27968 is a composite number with 28 divisors. Its prime factorisation is × 19 × 23. Divisors (28): 1, 2, 4, 8, 16, 19, 23, 32, 38, 46, 64, 76, 92, 152, 184, 304 … 27968.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27968: a Harshad number: divisible by its digit sum 32.
- 2
27968 is composite. Its prime factorisation is
- 3
The divisors add up to 60960; without 27968 itself that is 32992, so 27968 is abundant (32992 is more than 27968). Euler's totient φ(27968) = 12672 numbers up to 27968 share no factor with it.
- 4
The digits of 27968 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 121 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27968 = 2^{6} \times 19 \times 23 \]27968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 60960 |
| Euler totient φ(n) | 12672 |
| Square | 782209024 |
| Cube | 21876821983232 |
| Square root | 167.236360 (= 8√437) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 121 |
| Scientific notation | 2.7968 × |
27968 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand nine hundred and sixty-eight |
| Binary (base 2) | 110110101000000 |
| Octal (base 8) | 66500 |
| Hexadecimal (base 16) | 6D40 |
| Base 3 | 1102100212 |
| As time | 27968 seconds = 7 h 46 min 8 s |
Is 27968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27968 ÷ 2 = 13984) | 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 (27968 ÷ 4 = 6992) | 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 | No (remainder 2) | 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 (27968 ÷ 8 = 3496) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 27968 a prime number?
No. 27968 = × 19 × 23, so it is divisible by 2.
What are the factors of 27968?
1, 2, 4, 8, 16, 19, 23, 32, 38, 46, 64, 76, 92, 152, 184, 304, 368, 437, 608, 736, 874, 1216, 1472, 1748, 3496, 6992, 13984, 27968.
What is 27968 in binary?
110110101000000 (hexadecimal 6D40, octal 66500).
What is the square root of 27968?
About 167.2364, exactly 8√437.
Is 27968 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 27968?
27968 is a Harshad number: divisible by its digit sum 32.