The number 27997
27997 is the 3055th prime number. Its only divisors are 1 and 27997.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27997: the 3055th prime number.
- 2
27997 is prime, so its only factors are 1 and 27997. It is the 3055th prime; the next prime is 28001 and the one before is 27983.
- 3
The divisors add up to 27998; without 27997 itself that is 1, so 27997 is deficient (1 is less than 27997). Euler's totient φ(27997) = 27996 numbers up to 27997 share no factor with it.
- 4
The digits of 27997 add up to 34, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 134 steps to reach 1.
27997 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 27998 |
| Euler totient φ(n) | 27996 |
| Square | 783832009 |
| Cube | 21944944755973 |
| Square root | 167.323041 |
| Digit sum / digital root | 34 / 7 |
| Collatz steps to 1 | 134 |
| Scientific notation | 2.7997 × |
27997 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand nine hundred and ninety-seven |
| Binary (base 2) | 110110101011101 |
| Octal (base 8) | 66535 |
| Hexadecimal (base 16) | 6D5D |
| Base 3 | 1102101221 |
| As time | 27997 seconds = 7 h 46 min 37 s |
Is 27997 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 1) | 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 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | 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 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27997 a prime number?
Yes. 27997 is divisible only by 1 and itself.
What are the factors of 27997?
1, 27997.
What is 27997 in binary?
110110101011101 (hexadecimal 6D5D, octal 66535).
What is the square root of 27997?
About 167.3230.
Is 27997 divisible by 3?
No. Its digits add up to 34, which is not a multiple of 3.
What is special about the number 27997?
27997 is the 3055th prime number.