The number 13729
13729 is the 1625th prime number. Its only divisors are 1 and 13729.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13729: the 1625th prime number.
- 2
13729 is prime, so its only factors are 1 and 13729. It is the 1625th prime; the next prime is 13751 and the one before is 13723.
- 3
The divisors add up to 13730; without 13729 itself that is 1, so 13729 is deficient (1 is less than 13729). Euler's totient φ(13729) = 13728 numbers up to 13729 share no factor with it.
- 4
The digits of 13729 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
13729 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13730 |
| Euler totient φ(n) | 13728 |
| Square | 188485441 |
| Cube | 2587716619489 |
| Square root | 117.170815 |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.3729 × |
13729 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and twenty-nine |
| Binary (base 2) | 11010110100001 |
| Octal (base 8) | 32641 |
| Hexadecimal (base 16) | 35A1 |
| Base 3 | 200211111 |
| As time | 13729 seconds = 3 h 48 min 49 s |
Is 13729 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 1) | 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 13729 a prime number?
Yes. 13729 is divisible only by 1 and itself.
What are the factors of 13729?
1, 13729.
What is 13729 in binary?
11010110100001 (hexadecimal 35A1, octal 32641).
What is the square root of 13729?
About 117.1708.
Is 13729 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 13729?
13729 is the 1625th prime number.