The number 13788
13788 is a composite number with 18 divisors. Its prime factorisation is × × 383. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 383, 766, 1149, 1532, 2298, 3447, 4596 … 13788.
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How to work it out
- 1
13788 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13788 is composite. Its prime factorisation is
- 3
The divisors add up to 34944; without 13788 itself that is 21156, so 13788 is abundant (21156 is more than 13788). Euler's totient φ(13788) = 4584 numbers up to 13788 share no factor with it.
- 4
The digits of 13788 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 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13788 = 2^{2} \times 3^{2} \times 383 \]13788 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 34944 |
| Euler totient φ(n) | 4584 |
| Square | 190108944 |
| Cube | 2621222119872 |
| Square root | 117.422315 (= 6√383) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 58 |
| Scientific notation | 1.3788 × |
13788 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and eighty-eight |
| Binary (base 2) | 11010111011100 |
| Octal (base 8) | 32734 |
| Hexadecimal (base 16) | 35DC |
| Base 3 | 200220200 |
| As time | 13788 seconds = 3 h 49 min 48 s |
Is 13788 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13788 ÷ 2 = 6894) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13788 ÷ 3 = 4596) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13788 ÷ 4 = 3447) | 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 | Yes (13788 ÷ 6 = 2298) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | Yes (13788 ÷ 9 = 1532) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13788 ÷ 12 = 1149) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13788 a prime number?
No. 13788 = × × 383, so it is divisible by 2.
What are the factors of 13788?
1, 2, 3, 4, 6, 9, 12, 18, 36, 383, 766, 1149, 1532, 2298, 3447, 4596, 6894, 13788.
What is 13788 in binary?
11010111011100 (hexadecimal 35DC, octal 32734).
What is the square root of 13788?
About 117.4223, exactly 6√383.
Is 13788 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 13788?
It is a composite number with 18 divisors.