The number 48288
48288 is a composite number with 24 divisors. Its prime factorisation is × 3 × 503. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 503, 1006, 1509, 2012 … 48288.
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How to work it out
- 1
48288 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
48288 is composite. Its prime factorisation is
- 3
The divisors add up to 127008; without 48288 itself that is 78720, so 48288 is abundant (78720 is more than 48288). Euler's totient φ(48288) = 16064 numbers up to 48288 share no factor with it.
- 4
The digits of 48288 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 70 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48288 = 2^{5} \times 3 \times 503 \]48288 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 127008 |
| Euler totient φ(n) | 16064 |
| Square | 2331730944 |
| Cube | 112594623823872 |
| Square root | 219.745307 (= 4√3018) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 70 |
| Scientific notation | 4.8288 × |
48288 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand two hundred and eighty-eight |
| Binary (base 2) | 1011110010100000 |
| Octal (base 8) | 136240 |
| Hexadecimal (base 16) | BCA0 |
| Base 3 | 2110020110 |
| As time | 48288 seconds = 13 h 24 min 48 s |
Is 48288 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48288 ÷ 2 = 24144) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48288 ÷ 3 = 16096) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48288 ÷ 4 = 12072) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48288 ÷ 6 = 8048) | 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 (48288 ÷ 8 = 6036) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48288 ÷ 12 = 4024) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48288 a prime number?
No. 48288 = × 3 × 503, so it is divisible by 2.
What are the factors of 48288?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 503, 1006, 1509, 2012, 3018, 4024, 6036, 8048, 12072, 16096, 24144, 48288.
What is 48288 in binary?
1011110010100000 (hexadecimal BCA0, octal 136240).
What is the square root of 48288?
About 219.7453, exactly 4√3018.
Is 48288 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 48288?
It is a composite number with 24 divisors.