The number 27675
27675 is a binary palindrome (110110000011011). Its prime factorisation is × × 41. Divisors (24): 1, 3, 5, 9, 15, 25, 27, 41, 45, 75, 123, 135, 205, 225, 369, 615 … 27675.
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How to work it out
- 1
What is special about 27675: a binary palindrome (110110000011011); a Harshad number: divisible by its digit sum 27.
- 2
27675 is composite. Its prime factorisation is
- 3
The divisors add up to 52080; without 27675 itself that is 24405, so 27675 is deficient (24405 is less than 27675). Euler's totient φ(27675) = 14400 numbers up to 27675 share no factor with it.
- 4
The digits of 27675 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 139 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27675 = 3^{3} \times 5^{2} \times 41 \]27675 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 52080 |
| Euler totient φ(n) | 14400 |
| Square | 765905625 |
| Cube | 21196438171875 |
| Square root | 166.358048 (= 15√123) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 139 |
| Scientific notation | 2.7675 × |
27675 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand six hundred and seventy-five |
| Binary (base 2) | 110110000011011 |
| Octal (base 8) | 66033 |
| Hexadecimal (base 16) | 6C1B |
| Base 3 | 1101222000 |
| As time | 27675 seconds = 7 h 41 min 15 s |
Is 27675 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27675 ÷ 3 = 9225) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (27675 ÷ 5 = 5535) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (27675 ÷ 9 = 3075) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27675 a prime number?
No. 27675 = × × 41, so it is divisible by 3.
What are the factors of 27675?
1, 3, 5, 9, 15, 25, 27, 41, 45, 75, 123, 135, 205, 225, 369, 615, 675, 1025, 1107, 1845, 3075, 5535, 9225, 27675.
What is 27675 in binary?
110110000011011 (hexadecimal 6C1B, octal 66033).
What is the square root of 27675?
About 166.3580, exactly 15√123.
Is 27675 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 27675?
27675 is a binary palindrome (110110000011011); a Harshad number: divisible by its digit sum 27.