The number 83584
83584 is a composite number with 16 divisors. Its prime factorisation is × 653. Divisors (16): 1, 2, 4, 8, 16, 32, 64, 128, 653, 1306, 2612, 5224, 10448, 20896, 41792, 83584.
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How to work it out
- 1
83584 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
83584 is composite. Its prime factorisation is
- 3
The divisors add up to 166770; without 83584 itself that is 83186, so 83584 is deficient (83186 is less than 83584). Euler's totient φ(83584) = 41728 numbers up to 83584 share no factor with it.
- 4
The digits of 83584 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83584 = 2^{7} \times 653 \]83584 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 166770 |
| Euler totient φ(n) | 41728 |
| Square | 6986285056 |
| Cube | 583941650120704 |
| Square root | 289.108976 (= 8√1306) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 32 |
| Scientific notation | 8.3584 × |
83584 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand five hundred and eighty-four |
| Binary (base 2) | 10100011010000000 |
| Octal (base 8) | 243200 |
| Hexadecimal (base 16) | 14680 |
| Base 3 | 11020122201 |
| As time | 83584 seconds = 23 h 13 min 4 s |
Is 83584 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83584 ÷ 2 = 41792) | 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 (83584 ÷ 4 = 20896) | 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 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 (83584 ÷ 8 = 10448) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 6) | 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 83584 a prime number?
No. 83584 = × 653, so it is divisible by 2.
What are the factors of 83584?
1, 2, 4, 8, 16, 32, 64, 128, 653, 1306, 2612, 5224, 10448, 20896, 41792, 83584.
What is 83584 in binary?
10100011010000000 (hexadecimal 14680, octal 243200).
What is the square root of 83584?
About 289.1090, exactly 8√1306.
Is 83584 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 83584?
It is a composite number with 16 divisors.