The number 23584
23584 is a composite number with 24 divisors. Its prime factorisation is × 11 × 67. Divisors (24): 1, 2, 4, 8, 11, 16, 22, 32, 44, 67, 88, 134, 176, 268, 352, 536 … 23584.
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How to work it out
- 1
What is special about 23584: a Harshad number: divisible by its digit sum 22.
- 2
23584 is composite. Its prime factorisation is
- 3
The divisors add up to 51408; without 23584 itself that is 27824, so 23584 is abundant (27824 is more than 23584). Euler's totient φ(23584) = 10560 numbers up to 23584 share no factor with it.
- 4
The digits of 23584 add up to 22, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 144 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23584 = 2^{5} \times 11 \times 67 \]23584 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 51408 |
| Euler totient φ(n) | 10560 |
| Square | 556205056 |
| Cube | 13117540040704 |
| Square root | 153.570831 (= 4√1474) |
| Digit sum / digital root | 22 / 4 |
| Collatz steps to 1 | 144 |
| Scientific notation | 2.3584 × |
23584 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand five hundred and eighty-four |
| Binary (base 2) | 101110000100000 |
| Octal (base 8) | 56040 |
| Hexadecimal (base 16) | 5C20 |
| Base 3 | 1012100111 |
| As time | 23584 seconds = 6 h 33 min 4 s |
Is 23584 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23584 ÷ 2 = 11792) | 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 (23584 ÷ 4 = 5896) | 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 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 (23584 ÷ 8 = 2948) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 (23584 ÷ 11 = 2144) | 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 23584 a prime number?
No. 23584 = × 11 × 67, so it is divisible by 2.
What are the factors of 23584?
1, 2, 4, 8, 11, 16, 22, 32, 44, 67, 88, 134, 176, 268, 352, 536, 737, 1072, 1474, 2144, 2948, 5896, 11792, 23584.
What is 23584 in binary?
101110000100000 (hexadecimal 5C20, octal 56040).
What is the square root of 23584?
About 153.5708, exactly 4√1474.
Is 23584 divisible by 3?
No. Its digits add up to 22, which is not a multiple of 3.
What is special about the number 23584?
23584 is a Harshad number: divisible by its digit sum 22.