The number 13309
13309 is the 1580th prime number. Its only divisors are 1 and 13309.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13309: the 1580th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13309 is prime, so its only factors are 1 and 13309. It is the 1580th prime; the next prime is 13313 and the one before is 13297.
- 3
The divisors add up to 13310; without 13309 itself that is 1, so 13309 is deficient (1 is less than 13309). Euler's totient φ(13309) = 13308 numbers up to 13309 share no factor with it.
- 4
The digits of 13309 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
13309 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13310 |
| Euler totient φ(n) | 13308 |
| Square | 177129481 |
| Cube | 2357416262629 |
| Square root | 115.364639 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 76 |
| Scientific notation | 1.3309 × |
13309 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand three hundred and nine |
| Binary (base 2) | 11001111111101 |
| Octal (base 8) | 31775 |
| Hexadecimal (base 16) | 33FD |
| Base 3 | 200020221 |
| As time | 13309 seconds = 3 h 41 min 49 s |
Is 13309 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 2) | 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 7) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13309 a prime number?
Yes. 13309 is divisible only by 1 and itself.
What are the factors of 13309?
1, 13309.
What is 13309 in binary?
11001111111101 (hexadecimal 33FD, octal 31775).
What is the square root of 13309?
About 115.3646.
Is 13309 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 13309?
13309 is the 1580th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.