The number 8167
8167 is the 1025th prime number. Its only divisors are 1 and 8167.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8167: the 1025th prime number.
- 2
8167 is prime, so its only factors are 1 and 8167. It is the 1025th prime; the next prime is 8171 and the one before is 8161.
- 3
The divisors add up to 8168; without 8167 itself that is 1, so 8167 is deficient (1 is less than 8167). Euler's totient φ(8167) = 8166 numbers up to 8167 share no factor with it.
- 4
The digits of 8167 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 158 steps to reach 1.
8167 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 8168 |
| Euler totient φ(n) | 8166 |
| Square | 66699889 |
| Cube | 544737993463 |
| Square root | 90.371456 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 158 |
| Scientific notation | 8.167 × |
8167 in other forms
| Form | Value |
|---|---|
| In words | eight thousand one hundred and sixty-seven |
| Binary (base 2) | 1111111100111 |
| Octal (base 8) | 17747 |
| Hexadecimal (base 16) | 1FE7 |
| Base 3 | 102012111 |
| As time | 8167 seconds = 2 h 16 min 7 s |
Is 8167 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 5) | 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 8167 a prime number?
Yes. 8167 is divisible only by 1 and itself.
What are the factors of 8167?
1, 8167.
What is 8167 in binary?
1111111100111 (hexadecimal 1FE7, octal 17747).
What is the square root of 8167?
About 90.3715.
Is 8167 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 8167?
8167 is the 1025th prime number.