The number 38904
38904 is a composite number with 16 divisors. Its prime factorisation is × 3 × 1621. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 1621, 3242, 4863, 6484, 9726, 12968, 19452, 38904.
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How to work it out
- 1
What is special about 38904: a Harshad number: divisible by its digit sum 24.
- 2
38904 is composite. Its prime factorisation is
- 3
The divisors add up to 97320; without 38904 itself that is 58416, so 38904 is abundant (58416 is more than 38904). Euler's totient φ(38904) = 12960 numbers up to 38904 share no factor with it.
- 4
The digits of 38904 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38904 = 2^{3} \times 3 \times 1621 \]38904 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 97320 |
| Euler totient φ(n) | 12960 |
| Square | 1513521216 |
| Cube | 58882029387264 |
| Square root | 197.240969 (= 2√9726) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 93 |
| Scientific notation | 3.8904 × |
38904 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand nine hundred and four |
| Binary (base 2) | 1001011111111000 |
| Octal (base 8) | 113770 |
| Hexadecimal (base 16) | 97F8 |
| Base 3 | 1222100220 |
| As time | 38904 seconds = 10 h 48 min 24 s |
Is 38904 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38904 ÷ 2 = 19452) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38904 ÷ 3 = 12968) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38904 ÷ 4 = 9726) | 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 (38904 ÷ 6 = 6484) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (38904 ÷ 8 = 4863) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38904 ÷ 12 = 3242) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38904 a prime number?
No. 38904 = × 3 × 1621, so it is divisible by 2.
What are the factors of 38904?
1, 2, 3, 4, 6, 8, 12, 24, 1621, 3242, 4863, 6484, 9726, 12968, 19452, 38904.
What is 38904 in binary?
1001011111111000 (hexadecimal 97F8, octal 113770).
What is the square root of 38904?
About 197.2410, exactly 2√9726.
Is 38904 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 38904?
38904 is a Harshad number: divisible by its digit sum 24.