The number 38160
38160 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 53. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 38160.
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How to work it out
- 1
What is special about 38160: a Harshad number: divisible by its digit sum 18.
- 2
38160 is composite. Its prime factorisation is
- 3
The divisors add up to 130572; without 38160 itself that is 92412, so 38160 is abundant (92412 is more than 38160). Euler's totient φ(38160) = 9984 numbers up to 38160 share no factor with it.
- 4
The digits of 38160 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 106 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38160 = 2^{4} \times 3^{2} \times 5 \times 53 \]38160 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 130572 |
| Euler totient φ(n) | 9984 |
| Square | 1456185600 |
| Cube | 55568042496000 |
| Square root | 195.345847 (= 12√265) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 106 |
| Scientific notation | 3.816 × |
38160 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand one hundred and sixty |
| Binary (base 2) | 1001010100010000 |
| Octal (base 8) | 112420 |
| Hexadecimal (base 16) | 9510 |
| Base 3 | 1221100100 |
| As time | 38160 seconds = 10 h 36 min 0 s |
Is 38160 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38160 ÷ 2 = 19080) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38160 ÷ 3 = 12720) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38160 ÷ 4 = 9540) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (38160 ÷ 5 = 7632) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (38160 ÷ 6 = 6360) | 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 (38160 ÷ 8 = 4770) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (38160 ÷ 9 = 4240) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (38160 ÷ 10 = 3816) | 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 (38160 ÷ 12 = 3180) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38160 a prime number?
No. 38160 = × × 5 × 53, so it is divisible by 2.
What are the factors of 38160?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 53, 60, 72, 80, 90, 106, 120, 144, 159, 180, 212, 240, 265, 318, 360, 424, 477, 530, 636, 720, 795, 848, 954, 1060, 1272, 1590, 1908, 2120, 2385, 2544, 3180, 3816, 4240, 4770, 6360, 7632, 9540, 12720, 19080, 38160.
What is 38160 in binary?
1001010100010000 (hexadecimal 9510, octal 112420).
What is the square root of 38160?
About 195.3458, exactly 12√265.
Is 38160 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 38160?
38160 is a Harshad number: divisible by its digit sum 18.