The number 38784
38784 is a composite number with 32 divisors. Its prime factorisation is × 3 × 101. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 101, 128, 192 … 38784.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
38784 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
38784 is composite. Its prime factorisation is
- 3
The divisors add up to 104040; without 38784 itself that is 65256, so 38784 is abundant (65256 is more than 38784). Euler's totient φ(38784) = 12800 numbers up to 38784 share no factor with it.
- 4
The digits of 38784 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38784 = 2^{7} \times 3 \times 101 \]38784 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 104040 |
| Euler totient φ(n) | 12800 |
| Square | 1504198656 |
| Cube | 58338840674304 |
| Square root | 196.936538 (= 8√606) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 49 |
| Scientific notation | 3.8784 × |
38784 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand seven hundred and eighty-four |
| Binary (base 2) | 1001011110000000 |
| Octal (base 8) | 113600 |
| Hexadecimal (base 16) | 9780 |
| Base 3 | 1222012110 |
| As time | 38784 seconds = 10 h 46 min 24 s |
Is 38784 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38784 ÷ 2 = 19392) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38784 ÷ 3 = 12928) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38784 ÷ 4 = 9696) | 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 (38784 ÷ 6 = 6464) | 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 (38784 ÷ 8 = 4848) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38784 ÷ 12 = 3232) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38784 a prime number?
No. 38784 = × 3 × 101, so it is divisible by 2.
What are the factors of 38784?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 101, 128, 192, 202, 303, 384, 404, 606, 808, 1212, 1616, 2424, 3232, 4848, 6464, 9696, 12928, 19392, 38784.
What is 38784 in binary?
1001011110000000 (hexadecimal 9780, octal 113600).
What is the square root of 38784?
About 196.9365, exactly 8√606.
Is 38784 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 38784?
It is a composite number with 32 divisors.