The number 13986
13986 is a composite number with 32 divisors. Its prime factorisation is 2 × × 7 × 37. Divisors (32): 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 37, 42, 54, 63, 74, 111 … 13986.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13986: a Harshad number: divisible by its digit sum 27.
- 2
13986 is composite. Its prime factorisation is
- 3
The divisors add up to 36480; without 13986 itself that is 22494, so 13986 is abundant (22494 is more than 13986). Euler's totient φ(13986) = 3888 numbers up to 13986 share no factor with it.
- 4
The digits of 13986 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 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13986 = 2 \times 3^{3} \times 7 \times 37 \]13986 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 36480 |
| Euler totient φ(n) | 3888 |
| Square | 195608196 |
| Cube | 2735776229256 |
| Square root | 118.262420 (= 3√1554) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.3986 × |
13986 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and eighty-six |
| Binary (base 2) | 11011010100010 |
| Octal (base 8) | 33242 |
| Hexadecimal (base 16) | 36A2 |
| Base 3 | 201012000 |
| As time | 13986 seconds = 3 h 53 min 6 s |
Is 13986 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13986 ÷ 2 = 6993) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13986 ÷ 3 = 4662) | 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 (13986 ÷ 6 = 2331) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13986 ÷ 7 = 1998) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13986 ÷ 9 = 1554) | 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 5) | 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 13986 a prime number?
No. 13986 = 2 × × 7 × 37, so it is divisible by 2.
What are the factors of 13986?
1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 37, 42, 54, 63, 74, 111, 126, 189, 222, 259, 333, 378, 518, 666, 777, 999, 1554, 1998, 2331, 4662, 6993, 13986.
What is 13986 in binary?
11011010100010 (hexadecimal 36A2, octal 33242).
What is the square root of 13986?
About 118.2624, exactly 3√1554.
Is 13986 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 13986?
13986 is a Harshad number: divisible by its digit sum 27.