The number 38016
38016 is a composite number with 64 divisors. Its prime factorisation is × × 11. Divisors (64): 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 32, 33 … 38016.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 38016: a Harshad number: divisible by its digit sum 18.
- 2
38016 is composite. Its prime factorisation is
- 3
The divisors add up to 122400; without 38016 itself that is 84384, so 38016 is abundant (84384 is more than 38016). Euler's totient φ(38016) = 11520 numbers up to 38016 share no factor with it.
- 4
The digits of 38016 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 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38016 = 2^{7} \times 3^{3} \times 11 \]38016 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 122400 |
| Euler totient φ(n) | 11520 |
| Square | 1445216256 |
| Cube | 54941341188096 |
| Square root | 194.976922 (= 24√66) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 80 |
| Scientific notation | 3.8016 × |
38016 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand and sixteen |
| Binary (base 2) | 1001010010000000 |
| Octal (base 8) | 112200 |
| Hexadecimal (base 16) | 9480 |
| Base 3 | 1221011000 |
| As time | 38016 seconds = 10 h 33 min 36 s |
Is 38016 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38016 ÷ 2 = 19008) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38016 ÷ 3 = 12672) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38016 ÷ 4 = 9504) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (38016 ÷ 6 = 6336) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (38016 ÷ 8 = 4752) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (38016 ÷ 9 = 4224) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (38016 ÷ 11 = 3456) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38016 ÷ 12 = 3168) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38016 a prime number?
No. 38016 = × × 11, so it is divisible by 2.
What are the factors of 38016?
1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 32, 33, 36, 44, 48, 54, 64, 66, 72, 88, 96, 99, 108, 128, 132, 144, 176, 192, 198, 216, 264, 288, 297, 352, 384, 396, 432, 528, 576, 594, 704, 792, 864, 1056, 1152, 1188, 1408, 1584, 1728, 2112, 2376, 3168, 3456, 4224, 4752, 6336, 9504, 12672, 19008, 38016.
What is 38016 in binary?
1001010010000000 (hexadecimal 9480, octal 112200).
What is the square root of 38016?
About 194.9769, exactly 24√66.
Is 38016 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 38016?
38016 is a Harshad number: divisible by its digit sum 18.