The number 8009
8009 is a twin prime (8009 and 8011 are both prime) and the 1008th prime number. Its only divisors are 1 and 8009.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8009: a twin prime (8009 and 8011 are both prime); the 1008th prime number.
- 2
8009 is prime, so its only factors are 1 and 8009. It is the 1008th prime; the next prime is 8011 and the one before is 7993.
- 3
The divisors add up to 8010; without 8009 itself that is 1, so 8009 is deficient (1 is less than 8009). Euler's totient φ(8009) = 8008 numbers up to 8009 share no factor with it.
- 4
The digits of 8009 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
8009 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 8010 |
| Euler totient φ(n) | 8008 |
| Square | 64144081 |
| Cube | 513729944729 |
| Square root | 89.493016 |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 44 |
| Scientific notation | 8.009 × |
8009 in other forms
| Form | Value |
|---|---|
| In words | eight thousand and nine |
| Binary (base 2) | 1111101001001 |
| Octal (base 8) | 17511 |
| Hexadecimal (base 16) | 1F49 |
| Base 3 | 101222122 |
| As time | 8009 seconds = 2 h 13 min 29 s |
Is 8009 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 1) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 1) | 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 8009 a prime number?
Yes. 8009 is divisible only by 1 and itself.
What are the factors of 8009?
1, 8009.
What is 8009 in binary?
1111101001001 (hexadecimal 1F49, octal 17511).
What is the square root of 8009?
About 89.4930.
Is 8009 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 8009?
8009 is a twin prime (8009 and 8011 are both prime); the 1008th prime number.