The number 38736
38736 is a composite number with 30 divisors. Its prime factorisation is × × 269. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 269 … 38736.
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How to work it out
- 1
What is special about 38736: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
38736 is composite. Its prime factorisation is
- 3
The divisors add up to 108810; without 38736 itself that is 70074, so 38736 is abundant (70074 is more than 38736). Euler's totient φ(38736) = 12864 numbers up to 38736 share no factor with it.
- 4
The digits of 38736 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 23 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38736 = 2^{4} \times 3^{2} \times 269 \]38736 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 108810 |
| Euler totient φ(n) | 12864 |
| Square | 1500477696 |
| Cube | 58122504032256 |
| Square root | 196.814634 (= 12√269) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 23 |
| Scientific notation | 3.8736 × |
38736 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand seven hundred and thirty-six |
| Binary (base 2) | 1001011101010000 |
| Octal (base 8) | 113520 |
| Hexadecimal (base 16) | 9750 |
| Base 3 | 1222010200 |
| As time | 38736 seconds = 10 h 45 min 36 s |
Is 38736 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38736 ÷ 2 = 19368) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38736 ÷ 3 = 12912) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38736 ÷ 4 = 9684) | 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 (38736 ÷ 6 = 6456) | 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 (38736 ÷ 8 = 4842) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (38736 ÷ 9 = 4304) | 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 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38736 ÷ 12 = 3228) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38736 a prime number?
No. 38736 = × × 269, so it is divisible by 2.
What are the factors of 38736?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 269, 538, 807, 1076, 1614, 2152, 2421, 3228, 4304, 4842, 6456, 9684, 12912, 19368, 38736.
What is 38736 in binary?
1001011101010000 (hexadecimal 9750, octal 113520).
What is the square root of 38736?
About 196.8146, exactly 12√269.
Is 38736 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 38736?
38736 is a happy number: repeatedly adding the squares of its digits reaches 1.