The number 13728
13728 is a composite number with 48 divisors. Its prime factorisation is × 3 × 11 × 13. Divisors (48): 1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 32, 33, 39 … 13728.
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How to work it out
- 1
13728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13728 is composite. Its prime factorisation is
- 3
The divisors add up to 42336; without 13728 itself that is 28608, so 13728 is abundant (28608 is more than 13728). Euler's totient φ(13728) = 3840 numbers up to 13728 share no factor with it.
- 4
The digits of 13728 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13728 = 2^{5} \times 3 \times 11 \times 13 \]13728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 42336 |
| Euler totient φ(n) | 3840 |
| Square | 188457984 |
| Cube | 2587151204352 |
| Square root | 117.166548 (= 4√858) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.3728 × |
13728 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand seven hundred and twenty-eight |
| Binary (base 2) | 11010110100000 |
| Octal (base 8) | 32640 |
| Hexadecimal (base 16) | 35A0 |
| Base 3 | 200211110 |
| As time | 13728 seconds = 3 h 48 min 48 s |
Is 13728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13728 ÷ 2 = 6864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13728 ÷ 3 = 4576) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13728 ÷ 4 = 3432) | 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 (13728 ÷ 6 = 2288) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (13728 ÷ 8 = 1716) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | Yes (13728 ÷ 11 = 1248) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13728 ÷ 12 = 1144) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13728 a prime number?
No. 13728 = × 3 × 11 × 13, so it is divisible by 2.
What are the factors of 13728?
1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 32, 33, 39, 44, 48, 52, 66, 78, 88, 96, 104, 132, 143, 156, 176, 208, 264, 286, 312, 352, 416, 429, 528, 572, 624, 858, 1056, 1144, 1248, 1716, 2288, 3432, 4576, 6864, 13728.
What is 13728 in binary?
11010110100000 (hexadecimal 35A0, octal 32640).
What is the square root of 13728?
About 117.1665, exactly 4√858.
Is 13728 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 13728?
It is a composite number with 48 divisors.