The number 2309
2309 is a twin prime (2309 and 2311 are both prime) and the 343rd prime number. Its only divisors are 1 and 2309.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2309: a twin prime (2309 and 2311 are both prime); the 343rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
2309 is prime, so its only factors are 1 and 2309. It is the 343rd prime; the next prime is 2311 and the one before is 2297.
- 3
The divisors add up to 2310; without 2309 itself that is 1, so 2309 is deficient (1 is less than 2309). Euler's totient φ(2309) = 2308 numbers up to 2309 share no factor with it.
- 4
The digits of 2309 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
2309 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 2310 |
| Euler totient φ(n) | 2308 |
| Square | 5331481 |
| Cube | 12310389629 |
| Square root | 48.052055 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 32 |
| Scientific notation | 2.309 × |
2309 in other forms
| Form | Value |
|---|---|
| In words | two thousand three hundred and nine |
| Roman numerals | MMCCCIX |
| Binary (base 2) | 100100000101 |
| Octal (base 8) | 4405 |
| Hexadecimal (base 16) | 905 |
| Base 3 | 10011112 |
| As time | 2309 seconds = 38 min 29 s |
Is 2309 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 6) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 10) | 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 2309 a prime number?
Yes. 2309 is divisible only by 1 and itself.
What are the factors of 2309?
1, 2309.
What is 2309 in binary?
100100000101 (hexadecimal 905, octal 4405).
What is the square root of 2309?
About 48.0521.
What is 2309 in Roman numerals?
MMCCCIX.
Is 2309 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 2309?
2309 is a twin prime (2309 and 2311 are both prime); the 343rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.