The number 23328
23328 is a composite number with 42 divisors. Its prime factorisation is × . Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54 … 23328.
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How to work it out
- 1
What is special about 23328: a Harshad number: divisible by its digit sum 18.
- 2
23328 is composite. Its prime factorisation is
- 3
The divisors add up to 68859; without 23328 itself that is 45531, so 23328 is abundant (45531 is more than 23328). Euler's totient φ(23328) = 7776 numbers up to 23328 share no factor with it.
- 4
The digits of 23328 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 23328 = 2^{5} \times 3^{6} \]23328 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 68859 |
| Euler totient φ(n) | 7776 |
| Square | 544195584 |
| Cube | 12694994583552 |
| Square root | 152.735065 (= 108√2) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 38 |
| Scientific notation | 2.3328 × |
23328 in other forms
| Form | Value |
|---|---|
| In words | twenty-three thousand three hundred and twenty-eight |
| Binary (base 2) | 101101100100000 |
| Octal (base 8) | 55440 |
| Hexadecimal (base 16) | 5B20 |
| Base 3 | 1012000000 |
| As time | 23328 seconds = 6 h 28 min 48 s |
Is 23328 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (23328 ÷ 2 = 11664) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (23328 ÷ 3 = 7776) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (23328 ÷ 4 = 5832) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (23328 ÷ 6 = 3888) | 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 (23328 ÷ 8 = 2916) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (23328 ÷ 9 = 2592) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (23328 ÷ 12 = 1944) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 23328 a prime number?
No. 23328 = × , so it is divisible by 2.
What are the factors of 23328?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 729, 864, 972, 1296, 1458, 1944, 2592, 2916, 3888, 5832, 7776, 11664, 23328.
What is 23328 in binary?
101101100100000 (hexadecimal 5B20, octal 55440).
What is the square root of 23328?
About 152.7351, exactly 108√2.
Is 23328 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 23328?
23328 is a Harshad number: divisible by its digit sum 18.