The number 13584
13584 is a composite number with 20 divisors. Its prime factorisation is × 3 × 283. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 283, 566, 849, 1132, 1698, 2264 … 13584.
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How to work it out
- 1
13584 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13584 is composite. Its prime factorisation is
- 3
The divisors add up to 35216; without 13584 itself that is 21632, so 13584 is abundant (21632 is more than 13584). Euler's totient φ(13584) = 4512 numbers up to 13584 share no factor with it.
- 4
The digits of 13584 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 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13584 = 2^{4} \times 3 \times 283 \]13584 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 35216 |
| Euler totient φ(n) | 4512 |
| Square | 184525056 |
| Cube | 2506588360704 |
| Square root | 116.550418 (= 4√849) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 63 |
| Scientific notation | 1.3584 × |
13584 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and eighty-four |
| Binary (base 2) | 11010100010000 |
| Octal (base 8) | 32420 |
| Hexadecimal (base 16) | 3510 |
| Base 3 | 200122010 |
| As time | 13584 seconds = 3 h 46 min 24 s |
Is 13584 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13584 ÷ 2 = 6792) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13584 ÷ 3 = 4528) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13584 ÷ 4 = 3396) | 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 | Yes (13584 ÷ 6 = 2264) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (13584 ÷ 8 = 1698) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13584 ÷ 12 = 1132) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13584 a prime number?
No. 13584 = × 3 × 283, so it is divisible by 2.
What are the factors of 13584?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 283, 566, 849, 1132, 1698, 2264, 3396, 4528, 6792, 13584.
What is 13584 in binary?
11010100010000 (hexadecimal 3510, octal 32420).
What is the square root of 13584?
About 116.5504, exactly 4√849.
Is 13584 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 13584?
It is a composite number with 20 divisors.