The number 38688
38688 is a composite number with 48 divisors. Its prime factorisation is × 3 × 13 × 31. Divisors (48): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 31, 32, 39, 48, 52 … 38688.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
38688 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
38688 is composite. Its prime factorisation is
- 3
The divisors add up to 112896; without 38688 itself that is 74208, so 38688 is abundant (74208 is more than 38688). Euler's totient φ(38688) = 11520 numbers up to 38688 share no factor with it.
- 4
The digits of 38688 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38688 = 2^{5} \times 3 \times 13 \times 31 \]38688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 112896 |
| Euler totient φ(n) | 11520 |
| Square | 1496761344 |
| Cube | 57906702876672 |
| Square root | 196.692654 (= 4√2418) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 62 |
| Scientific notation | 3.8688 × |
38688 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand six hundred and eighty-eight |
| Binary (base 2) | 1001011100100000 |
| Octal (base 8) | 113440 |
| Hexadecimal (base 16) | 9720 |
| Base 3 | 1222001220 |
| As time | 38688 seconds = 10 h 44 min 48 s |
Is 38688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38688 ÷ 2 = 19344) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38688 ÷ 3 = 12896) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38688 ÷ 4 = 9672) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (38688 ÷ 6 = 6448) | 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 (38688 ÷ 8 = 4836) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38688 ÷ 12 = 3224) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38688 a prime number?
No. 38688 = × 3 × 13 × 31, so it is divisible by 2.
What are the factors of 38688?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 31, 32, 39, 48, 52, 62, 78, 93, 96, 104, 124, 156, 186, 208, 248, 312, 372, 403, 416, 496, 624, 744, 806, 992, 1209, 1248, 1488, 1612, 2418, 2976, 3224, 4836, 6448, 9672, 12896, 19344, 38688.
What is 38688 in binary?
1001011100100000 (hexadecimal 9720, octal 113440).
What is the square root of 38688?
About 196.6927, exactly 4√2418.
Is 38688 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 38688?
It is a composite number with 48 divisors.