The number 72768
72768 is a composite number with 28 divisors. Its prime factorisation is × 3 × 379. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 379, 758 … 72768.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
72768 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
72768 is composite. Its prime factorisation is
- 3
The divisors add up to 193040; without 72768 itself that is 120272, so 72768 is abundant (120272 is more than 72768). Euler's totient φ(72768) = 24192 numbers up to 72768 share no factor with it.
- 4
The digits of 72768 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 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72768 = 2^{6} \times 3 \times 379 \]72768 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 193040 |
| Euler totient φ(n) | 24192 |
| Square | 5295181824 |
| Cube | 385319790968832 |
| Square root | 269.755445 (= 8√1137) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 24 |
| Scientific notation | 7.2768 × |
72768 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand seven hundred and sixty-eight |
| Binary (base 2) | 10001110001000000 |
| Octal (base 8) | 216100 |
| Hexadecimal (base 16) | 11C40 |
| Base 3 | 10200211010 |
| As time | 72768 seconds = 20 h 12 min 48 s |
Is 72768 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72768 ÷ 2 = 36384) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72768 ÷ 3 = 24256) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72768 ÷ 4 = 18192) | 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 (72768 ÷ 6 = 12128) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (72768 ÷ 8 = 9096) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72768 ÷ 12 = 6064) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72768 a prime number?
No. 72768 = × 3 × 379, so it is divisible by 2.
What are the factors of 72768?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 379, 758, 1137, 1516, 2274, 3032, 4548, 6064, 9096, 12128, 18192, 24256, 36384, 72768.
What is 72768 in binary?
10001110001000000 (hexadecimal 11C40, octal 216100).
What is the square root of 72768?
About 269.7554, exactly 8√1137.
Is 72768 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 72768?
It is a composite number with 28 divisors.