The number 32384
32384 is a composite number with 32 divisors. Its prime factorisation is × 11 × 23. Divisors (32): 1, 2, 4, 8, 11, 16, 22, 23, 32, 44, 46, 64, 88, 92, 128, 176 … 32384.
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How to work it out
- 1
32384 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
32384 is composite. Its prime factorisation is
- 3
The divisors add up to 73440; without 32384 itself that is 41056, so 32384 is abundant (41056 is more than 32384). Euler's totient φ(32384) = 14080 numbers up to 32384 share no factor with it.
- 4
The digits of 32384 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 116 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32384 = 2^{7} \times 11 \times 23 \]32384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 73440 |
| Euler totient φ(n) | 14080 |
| Square | 1048723456 |
| Cube | 33961860399104 |
| Square root | 179.955550 (= 8√506) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 116 |
| Scientific notation | 3.2384 × |
32384 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand three hundred and eighty-four |
| Binary (base 2) | 111111010000000 |
| Octal (base 8) | 77200 |
| Hexadecimal (base 16) | 7E80 |
| Base 3 | 1122102102 |
| As time | 32384 seconds = 8 h 59 min 44 s |
Is 32384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32384 ÷ 2 = 16192) | 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 (32384 ÷ 4 = 8096) | 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 2) | 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 (32384 ÷ 8 = 4048) | 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 | Yes (32384 ÷ 11 = 2944) | 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 32384 a prime number?
No. 32384 = × 11 × 23, so it is divisible by 2.
What are the factors of 32384?
1, 2, 4, 8, 11, 16, 22, 23, 32, 44, 46, 64, 88, 92, 128, 176, 184, 253, 352, 368, 506, 704, 736, 1012, 1408, 1472, 2024, 2944, 4048, 8096, 16192, 32384.
What is 32384 in binary?
111111010000000 (hexadecimal 7E80, octal 77200).
What is the square root of 32384?
About 179.9556, exactly 8√506.
Is 32384 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 32384?
It is a composite number with 32 divisors.