The number 27084
27084 is a composite number with 24 divisors. Its prime factorisation is × 3 × 37 × 61. Divisors (24): 1, 2, 3, 4, 6, 12, 37, 61, 74, 111, 122, 148, 183, 222, 244, 366 … 27084.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27084: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
27084 is composite. Its prime factorisation is
- 3
The divisors add up to 65968; without 27084 itself that is 38884, so 27084 is abundant (38884 is more than 27084). Euler's totient φ(27084) = 8640 numbers up to 27084 share no factor with it.
- 4
The digits of 27084 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 183 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27084 = 2^{2} \times 3 \times 37 \times 61 \]27084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 65968 |
| Euler totient φ(n) | 8640 |
| Square | 733543056 |
| Cube | 19867280128704 |
| Square root | 164.572173 (= 2√6771) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 183 |
| Scientific notation | 2.7084 × |
27084 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand and eighty-four |
| Binary (base 2) | 110100111001100 |
| Octal (base 8) | 64714 |
| Hexadecimal (base 16) | 69CC |
| Base 3 | 1101011010 |
| As time | 27084 seconds = 7 h 31 min 24 s |
Is 27084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27084 ÷ 2 = 13542) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27084 ÷ 3 = 9028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27084 ÷ 4 = 6771) | 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 (27084 ÷ 6 = 4514) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27084 ÷ 12 = 2257) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27084 a prime number?
No. 27084 = × 3 × 37 × 61, so it is divisible by 2.
What are the factors of 27084?
1, 2, 3, 4, 6, 12, 37, 61, 74, 111, 122, 148, 183, 222, 244, 366, 444, 732, 2257, 4514, 6771, 9028, 13542, 27084.
What is 27084 in binary?
110100111001100 (hexadecimal 69CC, octal 64714).
What is the square root of 27084?
About 164.5722, exactly 2√6771.
Is 27084 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 27084?
27084 is a happy number: repeatedly adding the squares of its digits reaches 1.