The number 48096
48096 is a composite number with 36 divisors. Its prime factorisation is × × 167. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 48096.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
48096 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
48096 is composite. Its prime factorisation is
- 3
The divisors add up to 137592; without 48096 itself that is 89496, so 48096 is abundant (89496 is more than 48096). Euler's totient φ(48096) = 15936 numbers up to 48096 share no factor with it.
- 4
The digits of 48096 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 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48096 = 2^{5} \times 3^{2} \times 167 \]48096 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 137592 |
| Euler totient φ(n) | 15936 |
| Square | 2313225216 |
| Cube | 111256879988736 |
| Square root | 219.308003 (= 12√334) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 145 |
| Scientific notation | 4.8096 × |
48096 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand and ninety-six |
| Binary (base 2) | 1011101111100000 |
| Octal (base 8) | 135740 |
| Hexadecimal (base 16) | BBE0 |
| Base 3 | 2102222100 |
| As time | 48096 seconds = 13 h 21 min 36 s |
Is 48096 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48096 ÷ 2 = 24048) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48096 ÷ 3 = 16032) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48096 ÷ 4 = 12024) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48096 ÷ 6 = 8016) | 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 (48096 ÷ 8 = 6012) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (48096 ÷ 9 = 5344) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48096 ÷ 12 = 4008) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48096 a prime number?
No. 48096 = × × 167, so it is divisible by 2.
What are the factors of 48096?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 167, 288, 334, 501, 668, 1002, 1336, 1503, 2004, 2672, 3006, 4008, 5344, 6012, 8016, 12024, 16032, 24048, 48096.
What is 48096 in binary?
1011101111100000 (hexadecimal BBE0, octal 135740).
What is the square root of 48096?
About 219.3080, exactly 12√334.
Is 48096 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 48096?
It is a composite number with 36 divisors.