The number 38400
38400 is a composite number with 60 divisors. Its prime factorisation is × 3 × . Divisors (60): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32 … 38400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 38400: a Harshad number: divisible by its digit sum 15.
- 2
38400 is composite. Its prime factorisation is
- 3
The divisors add up to 126852; without 38400 itself that is 88452, so 38400 is abundant (88452 is more than 38400). Euler's totient φ(38400) = 10240 numbers up to 38400 share no factor with it.
- 4
The digits of 38400 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 23 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38400 = 2^{9} \times 3 \times 5^{2} \]38400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 126852 |
| Euler totient φ(n) | 10240 |
| Square | 1474560000 |
| Cube | 56623104000000 |
| Square root | 195.959179 (= 80√6) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 23 |
| Scientific notation | 3.84 × |
38400 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand four hundred |
| Binary (base 2) | 1001011000000000 |
| Octal (base 8) | 113000 |
| Hexadecimal (base 16) | 9600 |
| Base 3 | 1221200020 |
| As time | 38400 seconds = 10 h 40 min 0 s |
Is 38400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38400 ÷ 2 = 19200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38400 ÷ 3 = 12800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38400 ÷ 4 = 9600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (38400 ÷ 5 = 7680) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (38400 ÷ 6 = 6400) | 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 (38400 ÷ 8 = 4800) | 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 | Yes (38400 ÷ 10 = 3840) | 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 (38400 ÷ 12 = 3200) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38400 a prime number?
No. 38400 = × 3 × , so it is divisible by 2.
What are the factors of 38400?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 512, 600, 640, 768, 800, 960, 1200, 1280, 1536, 1600, 1920, 2400, 2560, 3200, 3840, 4800, 6400, 7680, 9600, 12800, 19200, 38400.
What is 38400 in binary?
1001011000000000 (hexadecimal 9600, octal 113000).
What is the square root of 38400?
About 195.9592, exactly 80√6.
Is 38400 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 38400?
38400 is a Harshad number: divisible by its digit sum 15.