The number 48864
48864 is a composite number with 24 divisors. Its prime factorisation is × 3 × 509. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 509, 1018, 1527, 2036 … 48864.
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How to work it out
- 1
48864 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
48864 is composite. Its prime factorisation is
- 3
The divisors add up to 128520; without 48864 itself that is 79656, so 48864 is abundant (79656 is more than 48864). Euler's totient φ(48864) = 16256 numbers up to 48864 share no factor with it.
- 4
The digits of 48864 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 158 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48864 = 2^{5} \times 3 \times 509 \]48864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 128520 |
| Euler totient φ(n) | 16256 |
| Square | 2387690496 |
| Cube | 116672108396544 |
| Square root | 221.052030 (= 4√3054) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 158 |
| Scientific notation | 4.8864 × |
48864 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand eight hundred and sixty-four |
| Binary (base 2) | 1011111011100000 |
| Octal (base 8) | 137340 |
| Hexadecimal (base 16) | BEE0 |
| Base 3 | 2111000210 |
| As time | 48864 seconds = 13 h 34 min 24 s |
Is 48864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48864 ÷ 2 = 24432) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48864 ÷ 3 = 16288) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48864 ÷ 4 = 12216) | 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 (48864 ÷ 6 = 8144) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (48864 ÷ 8 = 6108) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48864 ÷ 12 = 4072) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48864 a prime number?
No. 48864 = × 3 × 509, so it is divisible by 2.
What are the factors of 48864?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 509, 1018, 1527, 2036, 3054, 4072, 6108, 8144, 12216, 16288, 24432, 48864.
What is 48864 in binary?
1011111011100000 (hexadecimal BEE0, octal 137340).
What is the square root of 48864?
About 221.0520, exactly 4√3054.
Is 48864 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 48864?
It is a composite number with 24 divisors.