The number 13709
13709 is a twin prime (13709 and 13711 are both prime) and the 1621st prime number. Its only divisors are 1 and 13709.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13709: a twin prime (13709 and 13711 are both prime); the 1621st prime number.
- 2
13709 is prime, so its only factors are 1 and 13709. It is the 1621st prime; the next prime is 13711 and the one before is 13697.
- 3
The divisors add up to 13710; without 13709 itself that is 1, so 13709 is deficient (1 is less than 13709). Euler's totient φ(13709) = 13708 numbers up to 13709 share no factor with it.
- 4
The digits of 13709 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 32 steps to reach 1.
13709 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13710 |
| Euler totient φ(n) | 13708 |
| Square | 187936681 |
| Cube | 2576423959829 |
| Square root | 117.085439 |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 32 |
| Scientific notation | 1.3709 × |
13709 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and nine |
| Binary (base 2) | 11010110001101 |
| Octal (base 8) | 32615 |
| Hexadecimal (base 16) | 358D |
| Base 3 | 200210202 |
| As time | 13709 seconds = 3 h 48 min 29 s |
Is 13709 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 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 13709 a prime number?
Yes. 13709 is divisible only by 1 and itself.
What are the factors of 13709?
1, 13709.
What is 13709 in binary?
11010110001101 (hexadecimal 358D, octal 32615).
What is the square root of 13709?
About 117.0854.
Is 13709 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 13709?
13709 is a twin prime (13709 and 13711 are both prime); the 1621st prime number.