The number 27967
27967 is the 3053rd prime number. Its only divisors are 1 and 27967.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 27967: the 3053rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
27967 is prime, so its only factors are 1 and 27967. It is the 3053rd prime; the next prime is 27983 and the one before is 27961.
- 3
The divisors add up to 27968; without 27967 itself that is 1, so 27967 is deficient (1 is less than 27967). Euler's totient φ(27967) = 27966 numbers up to 27967 share no factor with it.
- 4
The digits of 27967 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 95 steps to reach 1.
27967 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 27968 |
| Euler totient φ(n) | 27966 |
| Square | 782153089 |
| Cube | 21874475440063 |
| Square root | 167.233370 |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 95 |
| Scientific notation | 2.7967 × |
27967 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand nine hundred and sixty-seven |
| Binary (base 2) | 110110100111111 |
| Octal (base 8) | 66477 |
| Hexadecimal (base 16) | 6D3F |
| Base 3 | 1102100211 |
| As time | 27967 seconds = 7 h 46 min 7 s |
Is 27967 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 3) | 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 2) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27967 a prime number?
Yes. 27967 is divisible only by 1 and itself.
What are the factors of 27967?
1, 27967.
What is 27967 in binary?
110110100111111 (hexadecimal 6D3F, octal 66477).
What is the square root of 27967?
About 167.2334.
Is 27967 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 27967?
27967 is the 3053rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.