The number 38304
38304 is a composite number with 72 divisors. Its prime factorisation is × × 7 × 19. Divisors (72): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 19, 21, 24, 28 … 38304.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 38304: a Harshad number: divisible by its digit sum 18.
- 2
38304 is composite. Its prime factorisation is
- 3
The divisors add up to 131040; without 38304 itself that is 92736, so 38304 is abundant (92736 is more than 38304). Euler's totient φ(38304) = 10368 numbers up to 38304 share no factor with it.
- 4
The digits of 38304 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 124 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38304 = 2^{5} \times 3^{2} \times 7 \times 19 \]38304 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 131040 |
| Euler totient φ(n) | 10368 |
| Square | 1467196416 |
| Cube | 56199491518464 |
| Square root | 195.714077 (= 12√266) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 124 |
| Scientific notation | 3.8304 × |
38304 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand three hundred and four |
| Binary (base 2) | 1001010110100000 |
| Octal (base 8) | 112640 |
| Hexadecimal (base 16) | 95A0 |
| Base 3 | 1221112200 |
| As time | 38304 seconds = 10 h 38 min 24 s |
Is 38304 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38304 ÷ 2 = 19152) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38304 ÷ 3 = 12768) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38304 ÷ 4 = 9576) | 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 | Yes (38304 ÷ 6 = 6384) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (38304 ÷ 7 = 5472) | 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 (38304 ÷ 8 = 4788) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (38304 ÷ 9 = 4256) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38304 ÷ 12 = 3192) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38304 a prime number?
No. 38304 = × × 7 × 19, so it is divisible by 2.
What are the factors of 38304?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 19, 21, 24, 28, 32, 36, 38, 42, 48, 56, 57, 63, 72, 76, 84, 96, 112, 114, 126, 133, 144, 152, 168, 171, 224, 228, 252, 266, 288, 304, 336, 342, 399, 456, 504, 532, 608, 672, 684, 798, 912, 1008, 1064, 1197, 1368, 1596, 1824, 2016, 2128, 2394, 2736, 3192, 4256, 4788, 5472, 6384, 9576, 12768, 19152, 38304.
What is 38304 in binary?
1001010110100000 (hexadecimal 95A0, octal 112640).
What is the square root of 38304?
About 195.7141, exactly 12√266.
Is 38304 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 38304?
38304 is a Harshad number: divisible by its digit sum 18.