The number 13689
13689 is a perfect square (117²). Its prime factorisation is × . Divisors (15): 1, 3, 9, 13, 27, 39, 81, 117, 169, 351, 507, 1053, 1521, 4563, 13689.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13689: a perfect square (117²); a Harshad number: divisible by its digit sum 27.
- 2
13689 is composite. Its prime factorisation is
- 3
The divisors add up to 22143; without 13689 itself that is 8454, so 13689 is deficient (8454 is less than 13689). Euler's totient φ(13689) = 8424 numbers up to 13689 share no factor with it.
- 4
The digits of 13689 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13689 = 3^{4} \times 13^{2} \]13689 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 22143 |
| Euler totient φ(n) | 8424 |
| Square | 187388721 |
| Cube | 2565164201769 |
| Square root | 117 |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3689 × |
| Perfect power |
13689 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand six hundred and eighty-nine |
| Binary (base 2) | 11010101111001 |
| Octal (base 8) | 32571 |
| Hexadecimal (base 16) | 3579 |
| Base 3 | 200210000 |
| As time | 13689 seconds = 3 h 48 min 9 s |
Is 13689 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 | Yes (13689 ÷ 3 = 4563) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | Yes (13689 ÷ 9 = 1521) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13689 a prime number?
No. 13689 = × , so it is divisible by 3.
What are the factors of 13689?
1, 3, 9, 13, 27, 39, 81, 117, 169, 351, 507, 1053, 1521, 4563, 13689.
What is 13689 in binary?
11010101111001 (hexadecimal 3579, octal 32571).
What is the square root of 13689?
117, because 117 × 117 = 13689.
Is 13689 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 13689?
13689 is a perfect square (117²); a Harshad number: divisible by its digit sum 27.