The number 13984
13984 is a composite number with 24 divisors. Its prime factorisation is × 19 × 23. Divisors (24): 1, 2, 4, 8, 16, 19, 23, 32, 38, 46, 76, 92, 152, 184, 304, 368 … 13984.
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How to work it out
- 1
13984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13984 is composite. Its prime factorisation is
- 3
The divisors add up to 30240; without 13984 itself that is 16256, so 13984 is abundant (16256 is more than 13984). Euler's totient φ(13984) = 6336 numbers up to 13984 share no factor with it.
- 4
The digits of 13984 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13984 = 2^{5} \times 19 \times 23 \]13984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 30240 |
| Euler totient φ(n) | 6336 |
| Square | 195552256 |
| Cube | 2734602747904 |
| Square root | 118.253964 (= 4√874) |
| Digit sum / digital root | 25 / 7 |
| Collatz steps to 1 | 120 |
| Scientific notation | 1.3984 × |
13984 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand nine hundred and eighty-four |
| Binary (base 2) | 11011010100000 |
| Octal (base 8) | 33240 |
| Hexadecimal (base 16) | 36A0 |
| Base 3 | 201011221 |
| As time | 13984 seconds = 3 h 53 min 4 s |
Is 13984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13984 ÷ 2 = 6992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13984 ÷ 4 = 3496) | 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 | No (remainder 4) | 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 | Yes (13984 ÷ 8 = 1748) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13984 a prime number?
No. 13984 = × 19 × 23, so it is divisible by 2.
What are the factors of 13984?
1, 2, 4, 8, 16, 19, 23, 32, 38, 46, 76, 92, 152, 184, 304, 368, 437, 608, 736, 874, 1748, 3496, 6992, 13984.
What is 13984 in binary?
11011010100000 (hexadecimal 36A0, octal 33240).
What is the square root of 13984?
About 118.2540, exactly 4√874.
Is 13984 divisible by 3?
No. Its digits add up to 25, which is not a multiple of 3.
What is special about the number 13984?
It is a composite number with 24 divisors.