The number 38320
38320 is a composite number with 20 divisors. Its prime factorisation is × 5 × 479. Divisors (20): 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 479, 958, 1916, 2395, 3832, 4790 … 38320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 38320: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.
- 2
38320 is composite. Its prime factorisation is
- 3
The divisors add up to 89280; without 38320 itself that is 50960, so 38320 is abundant (50960 is more than 38320). Euler's totient φ(38320) = 15296 numbers up to 38320 share no factor with it.
- 4
The digits of 38320 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38320 = 2^{4} \times 5 \times 479 \]38320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 89280 |
| Euler totient φ(n) | 15296 |
| Square | 1468422400 |
| Cube | 56269946368000 |
| Square root | 195.754949 (= 4√2395) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.832 × |
38320 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand three hundred and twenty |
| Binary (base 2) | 1001010110110000 |
| Octal (base 8) | 112660 |
| Hexadecimal (base 16) | 95B0 |
| Base 3 | 1221120021 |
| As time | 38320 seconds = 10 h 38 min 40 s |
Is 38320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38320 ÷ 2 = 19160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38320 ÷ 4 = 9580) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (38320 ÷ 5 = 7664) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (38320 ÷ 8 = 4790) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (38320 ÷ 10 = 3832) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38320 a prime number?
No. 38320 = × 5 × 479, so it is divisible by 2.
What are the factors of 38320?
1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 479, 958, 1916, 2395, 3832, 4790, 7664, 9580, 19160, 38320.
What is 38320 in binary?
1001010110110000 (hexadecimal 95B0, octal 112660).
What is the square root of 38320?
About 195.7549, exactly 4√2395.
Is 38320 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 38320?
38320 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.