The number 768
768 is a composite number with 18 divisors. Its prime factorisation is × 3. Divisors (18): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256 … 768.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
768 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
768 is composite. Its prime factorisation is
- 3
The divisors add up to 2044; without 768 itself that is 1276, so 768 is abundant (1276 is more than 768). Euler's totient φ(768) = 256 numbers up to 768 share no factor with it.
- 4
The digits of 768 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 15 steps to reach 1.
LaTeX source of the formulas on this page
\[ 768 = 2^{8} \times 3 \]768 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 2044 |
| Euler totient φ(n) | 256 |
| Square | 589824 |
| Cube | 452984832 |
| Square root | 27.712813 (= 16√3) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 15 |
| Scientific notation | 7.68 × |
768 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and sixty-eight |
| Roman numerals | DCCLXVIII |
| Binary (base 2) | 1100000000 |
| Octal (base 8) | 1400 |
| Hexadecimal (base 16) | 300 |
| Base 3 | 1001110 |
| As time | 768 seconds = 12 min 48 s |
Is 768 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (768 ÷ 2 = 384) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (768 ÷ 3 = 256) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (768 ÷ 4 = 192) | 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 (768 ÷ 6 = 128) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (768 ÷ 8 = 96) | 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 (768 ÷ 12 = 64) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 768 a prime number?
No. 768 = × 3, so it is divisible by 2.
What are the factors of 768?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768.
What is 768 in binary?
1100000000 (hexadecimal 300, octal 1400).
What is the square root of 768?
About 27.7128, exactly 16√3.
What is 768 in Roman numerals?
DCCLXVIII.
Is 768 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 768?
It is a composite number with 18 divisors.