The number 13684
13684 is a composite number with 12 divisors. Its prime factorisation is × 11 × 311. Divisors (12): 1, 2, 4, 11, 22, 44, 311, 622, 1244, 3421, 6842, 13684.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13684: a Harshad number: divisible by its digit sum 22.
- 2
13684 is composite. Its prime factorisation is
- 3
The divisors add up to 26208; without 13684 itself that is 12524, so 13684 is deficient (12524 is less than 13684). Euler's totient φ(13684) = 6200 numbers up to 13684 share no factor with it.
- 4
The digits of 13684 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.
LaTeX source of the formulas on this page
\[ 13684 = 2^{2} \times 11 \times 311 \]13684 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 26208 |
| Euler totient φ(n) | 6200 |
| Square | 187251856 |
| Cube | 2562354397504 |
| Square root | 116.978631 (= 2√3421) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.3684 × |
13684 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand six hundred and eighty-four |
| Binary (base 2) | 11010101110100 |
| Octal (base 8) | 32564 |
| Hexadecimal (base 16) | 3574 |
| Base 3 | 200202211 |
| As time | 13684 seconds = 3 h 48 min 4 s |
Is 13684 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13684 ÷ 2 = 6842) | 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 | Yes (13684 ÷ 4 = 3421) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 4) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (13684 ÷ 11 = 1244) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13684 a prime number?
No. 13684 = × 11 × 311, so it is divisible by 2.
What are the factors of 13684?
1, 2, 4, 11, 22, 44, 311, 622, 1244, 3421, 6842, 13684.
What is 13684 in binary?
11010101110100 (hexadecimal 3574, octal 32564).
What is the square root of 13684?
About 116.9786, exactly 2√3421.
Is 13684 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 13684?
13684 is a Harshad number: divisible by its digit sum 22.