The number 5309
5309 is the 704th prime number. Its only divisors are 1 and 5309.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5309: the 704th prime number.
- 2
5309 is prime, so its only factors are 1 and 5309. It is the 704th prime; the next prime is 5323 and the one before is 5303.
- 3
The divisors add up to 5310; without 5309 itself that is 1, so 5309 is deficient (1 is less than 5309). Euler's totient φ(5309) = 5308 numbers up to 5309 share no factor with it.
- 4
The digits of 5309 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 54 steps to reach 1.
5309 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 5310 |
| Euler totient φ(n) | 5308 |
| Square | 28185481 |
| Cube | 149636718629 |
| Square root | 72.862885 |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 54 |
| Scientific notation | 5.309 × |
5309 in other forms
| Form | Value |
|---|---|
| In words | five thousand three hundred and nine |
| Binary (base 2) | 1010010111101 |
| Octal (base 8) | 12275 |
| Hexadecimal (base 16) | 14BD |
| Base 3 | 21021122 |
| As time | 5309 seconds = 1 h 28 min 29 s |
Is 5309 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 5) | 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 7) | 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 5309 a prime number?
Yes. 5309 is divisible only by 1 and itself.
What are the factors of 5309?
1, 5309.
What is 5309 in binary?
1010010111101 (hexadecimal 14BD, octal 12275).
What is the square root of 5309?
About 72.8629.
Is 5309 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 5309?
5309 is the 704th prime number.