The number 83009
83009 is the 8108th prime number. Its only divisors are 1 and 83009.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83009: the 8108th prime number.
- 2
83009 is prime, so its only factors are 1 and 83009. It is the 8108th prime; the next prime is 83023 and the one before is 83003.
- 3
The divisors add up to 83010; without 83009 itself that is 1, so 83009 is deficient (1 is less than 83009). Euler's totient φ(83009) = 83008 numbers up to 83009 share no factor with it.
- 4
The digits of 83009 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
83009 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 83010 |
| Euler totient φ(n) | 83008 |
| Square | 6890494081 |
| Cube | 571973023169729 |
| Square root | 288.112825 |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.3009 × |
83009 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand and nine |
| Binary (base 2) | 10100010001000001 |
| Octal (base 8) | 242101 |
| Hexadecimal (base 16) | 14441 |
| Base 3 | 11012212102 |
| As time | 83009 seconds = 23 h 3 min 29 s |
Is 83009 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 3) | 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 2) | 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 3) | 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 83009 a prime number?
Yes. 83009 is divisible only by 1 and itself.
What are the factors of 83009?
1, 83009.
What is 83009 in binary?
10100010001000001 (hexadecimal 14441, octal 242101).
What is the square root of 83009?
About 288.1128.
Is 83009 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 83009?
83009 is the 8108th prime number.