The number 8209
8209 is the 1029th prime number. Its only divisors are 1 and 8209.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8209: the 1029th prime number.
- 2
8209 is prime, so its only factors are 1 and 8209. It is the 1029th prime; the next prime is 8219 and the one before is 8191.
- 3
The divisors add up to 8210; without 8209 itself that is 1, so 8209 is deficient (1 is less than 8209). Euler's totient φ(8209) = 8208 numbers up to 8209 share no factor with it.
- 4
The digits of 8209 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
8209 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 8210 |
| Euler totient φ(n) | 8208 |
| Square | 67387681 |
| Cube | 553185473329 |
| Square root | 90.603532 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 39 |
| Scientific notation | 8.209 × |
8209 in other forms
| Form | Value |
|---|---|
| In words | eight thousand two hundred and nine |
| Binary (base 2) | 10000000010001 |
| Octal (base 8) | 20021 |
| Hexadecimal (base 16) | 2011 |
| Base 3 | 102021001 |
| As time | 8209 seconds = 2 h 16 min 49 s |
Is 8209 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 4) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8209 a prime number?
Yes. 8209 is divisible only by 1 and itself.
What are the factors of 8209?
1, 8209.
What is 8209 in binary?
10000000010001 (hexadecimal 2011, octal 20021).
What is the square root of 8209?
About 90.6035.
Is 8209 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 8209?
8209 is the 1029th prime number.