The number 384
384 is a composite number with 16 divisors. Its prime factorisation is × 3. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
384 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
384 is composite. Its prime factorisation is
- 3
The divisors add up to 1020; without 384 itself that is 636, so 384 is abundant (636 is more than 384). Euler's totient φ(384) = 128 numbers up to 384 share no factor with it.
- 4
The digits of 384 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 14 steps to reach 1.
LaTeX source of the formulas on this page
\[ 384 = 2^{7} \times 3 \]384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 1020 |
| Euler totient φ(n) | 128 |
| Square | 147456 |
| Cube | 56623104 |
| Square root | 19.595918 (= 8√6) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 14 |
| Scientific notation | 3.84 × |
384 in other forms
| Form | Value |
|---|---|
| In words | three hundred and eighty-four |
| Roman numerals | CCCLXXXIV |
| Binary (base 2) | 110000000 |
| Octal (base 8) | 600 |
| Hexadecimal (base 16) | 180 |
| Base 3 | 112020 |
| As time | 384 seconds = 6 min 24 s |
Is 384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (384 ÷ 2 = 192) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (384 ÷ 3 = 128) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (384 ÷ 4 = 96) | 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 (384 ÷ 6 = 64) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (384 ÷ 8 = 48) | 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 | 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 (384 ÷ 12 = 32) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 384 a prime number?
No. 384 = × 3, so it is divisible by 2.
What are the factors of 384?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.
What is 384 in binary?
110000000 (hexadecimal 180, octal 600).
What is the square root of 384?
About 19.5959, exactly 8√6.
What is 384 in Roman numerals?
CCCLXXXIV.
Is 384 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 384?
It is a composite number with 16 divisors.