The number 13884
13884 is a composite number with 24 divisors. Its prime factorisation is × 3 × 13 × 89. Divisors (24): 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 89, 156, 178, 267, 356 … 13884.
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How to work it out
- 1
13884 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13884 is composite. Its prime factorisation is
- 3
The divisors add up to 35280; without 13884 itself that is 21396, so 13884 is abundant (21396 is more than 13884). Euler's totient φ(13884) = 4224 numbers up to 13884 share no factor with it.
- 4
The digits of 13884 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13884 = 2^{2} \times 3 \times 13 \times 89 \]13884 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 35280 |
| Euler totient φ(n) | 4224 |
| Square | 192765456 |
| Cube | 2676355591104 |
| Square root | 117.830387 (= 2√3471) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.3884 × |
13884 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand eight hundred and eighty-four |
| Binary (base 2) | 11011000111100 |
| Octal (base 8) | 33074 |
| Hexadecimal (base 16) | 363C |
| Base 3 | 201001020 |
| As time | 13884 seconds = 3 h 51 min 24 s |
Is 13884 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13884 ÷ 2 = 6942) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13884 ÷ 3 = 4628) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13884 ÷ 4 = 3471) | 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 (13884 ÷ 6 = 2314) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | No (remainder 6) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13884 ÷ 12 = 1157) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13884 a prime number?
No. 13884 = × 3 × 13 × 89, so it is divisible by 2.
What are the factors of 13884?
1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 89, 156, 178, 267, 356, 534, 1068, 1157, 2314, 3471, 4628, 6942, 13884.
What is 13884 in binary?
11011000111100 (hexadecimal 363C, octal 33074).
What is the square root of 13884?
About 117.8304, exactly 2√3471.
Is 13884 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 13884?
It is a composite number with 24 divisors.