The number 13688
13688 is a composite number with 16 divisors. Its prime factorisation is × 29 × 59. Divisors (16): 1, 2, 4, 8, 29, 58, 59, 116, 118, 232, 236, 472, 1711, 3422, 6844, 13688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13688 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13688 is composite. Its prime factorisation is
- 3
The divisors add up to 27000; without 13688 itself that is 13312, so 13688 is deficient (13312 is less than 13688). Euler's totient φ(13688) = 6496 numbers up to 13688 share no factor with it.
- 4
The digits of 13688 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13688 = 2^{3} \times 29 \times 59 \]13688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 27000 |
| Euler totient φ(n) | 6496 |
| Square | 187361344 |
| Cube | 2564602076672 |
| Square root | 116.995726 (= 2√3422) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 151 |
| Scientific notation | 1.3688 × |
13688 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand six hundred and eighty-eight |
| Binary (base 2) | 11010101111000 |
| Octal (base 8) | 32570 |
| Hexadecimal (base 16) | 3578 |
| Base 3 | 200202222 |
| As time | 13688 seconds = 3 h 48 min 8 s |
Is 13688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13688 ÷ 2 = 6844) | 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 | Yes (13688 ÷ 4 = 3422) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 | Yes (13688 ÷ 8 = 1711) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13688 a prime number?
No. 13688 = × 29 × 59, so it is divisible by 2.
What are the factors of 13688?
1, 2, 4, 8, 29, 58, 59, 116, 118, 232, 236, 472, 1711, 3422, 6844, 13688.
What is 13688 in binary?
11010101111000 (hexadecimal 3578, octal 32570).
What is the square root of 13688?
About 116.9957, exactly 2√3422.
Is 13688 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 13688?
It is a composite number with 16 divisors.