The number 48960
48960 is a composite number with 84 divisors. Its prime factorisation is × × 5 × 17. Divisors (84): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24 … 48960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
48960 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
48960 is composite. Its prime factorisation is
- 3
The divisors add up to 178308; without 48960 itself that is 129348, so 48960 is abundant (129348 is more than 48960). Euler's totient φ(48960) = 12288 numbers up to 48960 share no factor with it.
- 4
The digits of 48960 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 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48960 = 2^{6} \times 3^{2} \times 5 \times 17 \]48960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 84 |
| Sum of divisors | 178308 |
| Euler totient φ(n) | 12288 |
| Square | 2397081600 |
| Cube | 117361115136000 |
| Square root | 221.269067 (= 24√85) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.896 × |
48960 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand nine hundred and sixty |
| Binary (base 2) | 1011111101000000 |
| Octal (base 8) | 137500 |
| Hexadecimal (base 16) | BF40 |
| Base 3 | 2111011100 |
| As time | 48960 seconds = 13 h 36 min 0 s |
Is 48960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48960 ÷ 2 = 24480) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48960 ÷ 3 = 16320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48960 ÷ 4 = 12240) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (48960 ÷ 5 = 9792) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48960 ÷ 6 = 8160) | 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 (48960 ÷ 8 = 6120) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (48960 ÷ 9 = 5440) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (48960 ÷ 10 = 4896) | 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 (48960 ÷ 12 = 4080) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48960 a prime number?
No. 48960 = × × 5 × 17, so it is divisible by 2.
What are the factors of 48960?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 30, 32, 34, 36, 40, 45, 48, 51, 60, 64, 68, 72, 80, 85, 90, 96, 102, 120, 136, 144, 153, 160, 170, 180, 192, 204, 240, 255, 272, 288, 306, 320, 340, 360, 408, 480, 510, 544, 576, 612, 680, 720, 765, 816, 960, 1020, 1088, 1224, 1360, 1440, 1530, 1632, 2040, 2448, 2720, 2880, 3060, 3264, 4080, 4896, 5440, 6120, 8160, 9792, 12240, 16320, 24480, 48960.
What is 48960 in binary?
1011111101000000 (hexadecimal BF40, octal 137500).
What is the square root of 48960?
About 221.2691, exactly 24√85.
Is 48960 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 48960?
It is a composite number with 84 divisors.