The number 27328
27328 is a composite number with 28 divisors. Its prime factorisation is × 7 × 61. Divisors (28): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 61, 64, 112, 122, 224, 244 … 27328.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27328: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
27328 is composite. Its prime factorisation is
- 3
The divisors add up to 62992; without 27328 itself that is 35664, so 27328 is abundant (35664 is more than 27328). Euler's totient φ(27328) = 11520 numbers up to 27328 share no factor with it.
- 4
The digits of 27328 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 59 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27328 = 2^{6} \times 7 \times 61 \]27328 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 62992 |
| Euler totient φ(n) | 11520 |
| Square | 746819584 |
| Cube | 20409085591552 |
| Square root | 165.311827 (= 8√427) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 59 |
| Scientific notation | 2.7328 × |
27328 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand three hundred and twenty-eight |
| Binary (base 2) | 110101011000000 |
| Octal (base 8) | 65300 |
| Hexadecimal (base 16) | 6AC0 |
| Base 3 | 1101111011 |
| As time | 27328 seconds = 7 h 35 min 28 s |
Is 27328 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27328 ÷ 2 = 13664) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27328 ÷ 4 = 6832) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (27328 ÷ 7 = 3904) | 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 (27328 ÷ 8 = 3416) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27328 a prime number?
No. 27328 = × 7 × 61, so it is divisible by 2.
What are the factors of 27328?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 61, 64, 112, 122, 224, 244, 427, 448, 488, 854, 976, 1708, 1952, 3416, 3904, 6832, 13664, 27328.
What is 27328 in binary?
110101011000000 (hexadecimal 6AC0, octal 65300).
What is the square root of 27328?
About 165.3118, exactly 8√427.
Is 27328 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 27328?
27328 is a happy number: repeatedly adding the squares of its digits reaches 1.