The number 27509
27509 is the 3005th prime number. Its only divisors are 1 and 27509.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27509: the 3005th prime number.
- 2
27509 is prime, so its only factors are 1 and 27509. It is the 3005th prime; the next prime is 27527 and the one before is 27487.
- 3
The divisors add up to 27510; without 27509 itself that is 1, so 27509 is deficient (1 is less than 27509). Euler's totient φ(27509) = 27508 numbers up to 27509 share no factor with it.
- 4
The digits of 27509 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 152 steps to reach 1.
27509 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 27510 |
| Euler totient φ(n) | 27508 |
| Square | 756745081 |
| Cube | 20817300433229 |
| Square root | 165.858373 |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 152 |
| Scientific notation | 2.7509 × |
27509 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand five hundred and nine |
| Binary (base 2) | 110101101110101 |
| Octal (base 8) | 65565 |
| Hexadecimal (base 16) | 6B75 |
| Base 3 | 1101201212 |
| As time | 27509 seconds = 7 h 38 min 29 s |
Is 27509 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 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 5) | 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 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27509 a prime number?
Yes. 27509 is divisible only by 1 and itself.
What are the factors of 27509?
1, 27509.
What is 27509 in binary?
110101101110101 (hexadecimal 6B75, octal 65565).
What is the square root of 27509?
About 165.8584.
Is 27509 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 27509?
27509 is the 3005th prime number.