The number 38664
38664 is a composite number with 32 divisors. Its prime factorisation is × × 179. Divisors (32): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 179 … 38664.
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How to work it out
- 1
What is special about 38664: a Harshad number: divisible by its digit sum 27.
- 2
38664 is composite. Its prime factorisation is
- 3
The divisors add up to 108000; without 38664 itself that is 69336, so 38664 is abundant (69336 is more than 38664). Euler's totient φ(38664) = 12816 numbers up to 38664 share no factor with it.
- 4
The digits of 38664 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 75 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38664 = 2^{3} \times 3^{3} \times 179 \]38664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 108000 |
| Euler totient φ(n) | 12816 |
| Square | 1494904896 |
| Cube | 57799002898944 |
| Square root | 196.631635 (= 6√1074) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 75 |
| Scientific notation | 3.8664 × |
38664 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand six hundred and sixty-four |
| Binary (base 2) | 1001011100001000 |
| Octal (base 8) | 113410 |
| Hexadecimal (base 16) | 9708 |
| Base 3 | 1222001000 |
| As time | 38664 seconds = 10 h 44 min 24 s |
Is 38664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38664 ÷ 2 = 19332) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38664 ÷ 3 = 12888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38664 ÷ 4 = 9666) | 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 (38664 ÷ 6 = 6444) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (38664 ÷ 8 = 4833) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (38664 ÷ 9 = 4296) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38664 ÷ 12 = 3222) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38664 a prime number?
No. 38664 = × × 179, so it is divisible by 2.
What are the factors of 38664?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 179, 216, 358, 537, 716, 1074, 1432, 1611, 2148, 3222, 4296, 4833, 6444, 9666, 12888, 19332, 38664.
What is 38664 in binary?
1001011100001000 (hexadecimal 9708, octal 113410).
What is the square root of 38664?
About 196.6316, exactly 6√1074.
Is 38664 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 38664?
38664 is a Harshad number: divisible by its digit sum 27.