The number 17984
17984 is a composite number with 14 divisors. Its prime factorisation is × 281. Divisors (14): 1, 2, 4, 8, 16, 32, 64, 281, 562, 1124, 2248, 4496, 8992, 17984.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
17984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
17984 is composite. Its prime factorisation is
- 3
The divisors add up to 35814; without 17984 itself that is 17830, so 17984 is deficient (17830 is less than 17984). Euler's totient φ(17984) = 8960 numbers up to 17984 share no factor with it.
- 4
The digits of 17984 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17984 = 2^{6} \times 281 \]17984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 35814 |
| Euler totient φ(n) | 8960 |
| Square | 323424256 |
| Cube | 5816461819904 |
| Square root | 134.104437 (= 8√281) |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 48 |
| Scientific notation | 1.7984 × |
17984 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand nine hundred and eighty-four |
| Binary (base 2) | 100011001000000 |
| Octal (base 8) | 43100 |
| Hexadecimal (base 16) | 4640 |
| Base 3 | 220200002 |
| As time | 17984 seconds = 4 h 59 min 44 s |
Is 17984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17984 ÷ 2 = 8992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17984 ÷ 4 = 4496) | 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 2) | 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 (17984 ÷ 8 = 2248) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17984 a prime number?
No. 17984 = × 281, so it is divisible by 2.
What are the factors of 17984?
1, 2, 4, 8, 16, 32, 64, 281, 562, 1124, 2248, 4496, 8992, 17984.
What is 17984 in binary?
100011001000000 (hexadecimal 4640, octal 43100).
What is the square root of 17984?
About 134.1044, exactly 8√281.
Is 17984 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 17984?
It is a composite number with 14 divisors.