The number 48768
48768 is a composite number with 32 divisors. Its prime factorisation is × 3 × 127. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 127, 128, 192 … 48768.
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How to work it out
- 1
48768 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
48768 is composite. Its prime factorisation is
- 3
The divisors add up to 130560; without 48768 itself that is 81792, so 48768 is abundant (81792 is more than 48768). Euler's totient φ(48768) = 16128 numbers up to 48768 share no factor with it.
- 4
The digits of 48768 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 114 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48768 = 2^{7} \times 3 \times 127 \]48768 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 130560 |
| Euler totient φ(n) | 16128 |
| Square | 2378317824 |
| Cube | 115985803640832 |
| Square root | 220.834780 (= 8√762) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 114 |
| Scientific notation | 4.8768 × |
48768 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand seven hundred and sixty-eight |
| Binary (base 2) | 1011111010000000 |
| Octal (base 8) | 137200 |
| Hexadecimal (base 16) | BE80 |
| Base 3 | 2110220020 |
| As time | 48768 seconds = 13 h 32 min 48 s |
Is 48768 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48768 ÷ 2 = 24384) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48768 ÷ 3 = 16256) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48768 ÷ 4 = 12192) | 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 (48768 ÷ 6 = 8128) | 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 (48768 ÷ 8 = 6096) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48768 ÷ 12 = 4064) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48768 a prime number?
No. 48768 = × 3 × 127, so it is divisible by 2.
What are the factors of 48768?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 127, 128, 192, 254, 381, 384, 508, 762, 1016, 1524, 2032, 3048, 4064, 6096, 8128, 12192, 16256, 24384, 48768.
What is 48768 in binary?
1011111010000000 (hexadecimal BE80, octal 137200).
What is the square root of 48768?
About 220.8348, exactly 8√762.
Is 48768 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 48768?
It is a composite number with 32 divisors.