The number 48384
48384 is a palindrome: it reads 48384 backwards too. Its prime factorisation is × × 7. Divisors (72): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28 … 48384.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48384: a palindrome: it reads 48384 backwards too; a Harshad number: divisible by its digit sum 27.
- 2
48384 is composite. Its prime factorisation is
- 3
The divisors add up to 163520; without 48384 itself that is 115136, so 48384 is abundant (115136 is more than 48384). Euler's totient φ(48384) = 13824 numbers up to 48384 share no factor with it.
- 4
The digits of 48384 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 114 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48384 = 2^{8} \times 3^{3} \times 7 \]48384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 163520 |
| Euler totient φ(n) | 13824 |
| Square | 2341011456 |
| Cube | 113267498287104 |
| Square root | 219.963633 (= 48√21) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 114 |
| Scientific notation | 4.8384 × |
48384 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand three hundred and eighty-four |
| Binary (base 2) | 1011110100000000 |
| Octal (base 8) | 136400 |
| Hexadecimal (base 16) | BD00 |
| Base 3 | 2110101000 |
| As time | 48384 seconds = 13 h 26 min 24 s |
Is 48384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48384 ÷ 2 = 24192) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48384 ÷ 3 = 16128) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48384 ÷ 4 = 12096) | 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 (48384 ÷ 6 = 8064) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (48384 ÷ 7 = 6912) | 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 (48384 ÷ 8 = 6048) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (48384 ÷ 9 = 5376) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48384 ÷ 12 = 4032) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48384 a prime number?
No. 48384 = × × 7, so it is divisible by 2.
What are the factors of 48384?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 64, 72, 84, 96, 108, 112, 126, 128, 144, 168, 189, 192, 216, 224, 252, 256, 288, 336, 378, 384, 432, 448, 504, 576, 672, 756, 768, 864, 896, 1008, 1152, 1344, 1512, 1728, 1792, 2016, 2304, 2688, 3024, 3456, 4032, 5376, 6048, 6912, 8064, 12096, 16128, 24192, 48384.
What is 48384 in binary?
1011110100000000 (hexadecimal BD00, octal 136400).
What is the square root of 48384?
About 219.9636, exactly 48√21.
Is 48384 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 48384?
48384 is a palindrome: it reads 48384 backwards too; a Harshad number: divisible by its digit sum 27.