The number 38064
38064 is a composite number with 40 divisors. Its prime factorisation is × 3 × 13 × 61. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 61, 78 … 38064.
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How to work it out
- 1
38064 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
38064 is composite. Its prime factorisation is
- 3
The divisors add up to 107632; without 38064 itself that is 69568, so 38064 is abundant (69568 is more than 38064). Euler's totient φ(38064) = 11520 numbers up to 38064 share no factor with it.
- 4
The digits of 38064 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38064 = 2^{4} \times 3 \times 13 \times 61 \]38064 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 107632 |
| Euler totient φ(n) | 11520 |
| Square | 1448868096 |
| Cube | 55149715206144 |
| Square root | 195.099974 (= 4√2379) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 80 |
| Scientific notation | 3.8064 × |
38064 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand and sixty-four |
| Binary (base 2) | 1001010010110000 |
| Octal (base 8) | 112260 |
| Hexadecimal (base 16) | 94B0 |
| Base 3 | 1221012210 |
| As time | 38064 seconds = 10 h 34 min 24 s |
Is 38064 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38064 ÷ 2 = 19032) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38064 ÷ 3 = 12688) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38064 ÷ 4 = 9516) | 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 (38064 ÷ 6 = 6344) | 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 (38064 ÷ 8 = 4758) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38064 ÷ 12 = 3172) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38064 a prime number?
No. 38064 = × 3 × 13 × 61, so it is divisible by 2.
What are the factors of 38064?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 61, 78, 104, 122, 156, 183, 208, 244, 312, 366, 488, 624, 732, 793, 976, 1464, 1586, 2379, 2928, 3172, 4758, 6344, 9516, 12688, 19032, 38064.
What is 38064 in binary?
1001010010110000 (hexadecimal 94B0, octal 112260).
What is the square root of 38064?
About 195.1000, exactly 4√2379.
Is 38064 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 38064?
It is a composite number with 40 divisors.