The number 27804
27804 is a composite number with 24 divisors. Its prime factorisation is × 3 × 7 × 331. Divisors (24): 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 331, 662, 993, 1324 … 27804.
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How to work it out
- 1
What is special about 27804: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
27804 is composite. Its prime factorisation is
- 3
The divisors add up to 74368; without 27804 itself that is 46564, so 27804 is abundant (46564 is more than 27804). Euler's totient φ(27804) = 7920 numbers up to 27804 share no factor with it.
- 4
The digits of 27804 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 113 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27804 = 2^{2} \times 3 \times 7 \times 331 \]27804 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 74368 |
| Euler totient φ(n) | 7920 |
| Square | 773062416 |
| Cube | 21494227414464 |
| Square root | 166.745315 (= 2√6951) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 113 |
| Scientific notation | 2.7804 × |
27804 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand eight hundred and four |
| Binary (base 2) | 110110010011100 |
| Octal (base 8) | 66234 |
| Hexadecimal (base 16) | 6C9C |
| Base 3 | 1102010210 |
| As time | 27804 seconds = 7 h 43 min 24 s |
Is 27804 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27804 ÷ 2 = 13902) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27804 ÷ 3 = 9268) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27804 ÷ 4 = 6951) | 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 (27804 ÷ 6 = 4634) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (27804 ÷ 7 = 3972) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27804 ÷ 12 = 2317) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27804 a prime number?
No. 27804 = × 3 × 7 × 331, so it is divisible by 2.
What are the factors of 27804?
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 331, 662, 993, 1324, 1986, 2317, 3972, 4634, 6951, 9268, 13902, 27804.
What is 27804 in binary?
110110010011100 (hexadecimal 6C9C, octal 66234).
What is the square root of 27804?
About 166.7453, exactly 2√6951.
Is 27804 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 27804?
27804 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.