The number 13806
13806 is a composite number with 24 divisors. Its prime factorisation is 2 × × 13 × 59. Divisors (24): 1, 2, 3, 6, 9, 13, 18, 26, 39, 59, 78, 117, 118, 177, 234, 354 … 13806.
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How to work it out
- 1
What is special about 13806: a Harshad number: divisible by its digit sum 18.
- 2
13806 is composite. Its prime factorisation is
- 3
The divisors add up to 32760; without 13806 itself that is 18954, so 13806 is abundant (18954 is more than 13806). Euler's totient φ(13806) = 4176 numbers up to 13806 share no factor with it.
- 4
The digits of 13806 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13806 = 2 \times 3^{2} \times 13 \times 59 \]13806 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 32760 |
| Euler totient φ(n) | 4176 |
| Square | 190605636 |
| Cube | 2631501410616 |
| Square root | 117.498936 (= 3√1534) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.3806 × |
13806 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and six |
| Binary (base 2) | 11010111101110 |
| Octal (base 8) | 32756 |
| Hexadecimal (base 16) | 35EE |
| Base 3 | 200221100 |
| As time | 13806 seconds = 3 h 50 min 6 s |
Is 13806 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13806 ÷ 2 = 6903) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13806 ÷ 3 = 4602) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (13806 ÷ 6 = 2301) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13806 ÷ 9 = 1534) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13806 a prime number?
No. 13806 = 2 × × 13 × 59, so it is divisible by 2.
What are the factors of 13806?
1, 2, 3, 6, 9, 13, 18, 26, 39, 59, 78, 117, 118, 177, 234, 354, 531, 767, 1062, 1534, 2301, 4602, 6903, 13806.
What is 13806 in binary?
11010111101110 (hexadecimal 35EE, octal 32756).
What is the square root of 13806?
About 117.4989, exactly 3√1534.
Is 13806 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13806?
13806 is a Harshad number: divisible by its digit sum 18.