The number 96768
96768 is a composite number with 80 divisors. Its prime factorisation is × × 7. Divisors (80): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28 … 96768.
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How to work it out
- 1
What is special about 96768: a Harshad number: divisible by its digit sum 36.
- 2
96768 is composite. Its prime factorisation is
- 3
The divisors add up to 327360; without 96768 itself that is 230592, so 96768 is abundant (230592 is more than 96768). Euler's totient φ(96768) = 27648 numbers up to 96768 share no factor with it.
- 4
The digits of 96768 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 115 steps to reach 1.
LaTeX source of the formulas on this page
\[ 96768 = 2^{9} \times 3^{3} \times 7 \]96768 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 327360 |
| Euler totient φ(n) | 27648 |
| Square | 9364045824 |
| Cube | 906139986296832 |
| Square root | 311.075554 (= 48√42) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 115 |
| Scientific notation | 9.6768 × |
96768 in other forms
| Form | Value |
|---|---|
| In words | ninety-six thousand seven hundred and sixty-eight |
| Binary (base 2) | 10111101000000000 |
| Octal (base 8) | 275000 |
| Hexadecimal (base 16) | 17A00 |
| Base 3 | 11220202000 |
| As time | 96768 seconds = 26 h 52 min 48 s |
Is 96768 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (96768 ÷ 2 = 48384) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (96768 ÷ 3 = 32256) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (96768 ÷ 4 = 24192) | 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 (96768 ÷ 6 = 16128) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (96768 ÷ 7 = 13824) | 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 (96768 ÷ 8 = 12096) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (96768 ÷ 9 = 10752) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (96768 ÷ 12 = 8064) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 96768 a prime number?
No. 96768 = × × 7, so it is divisible by 2.
What are the factors of 96768?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 64, 72, 84, 96, 108, 112, 126, 128, 144, 168, 189, 192, 216, 224, 252, 256, 288, 336, 378, 384, 432, 448, 504, 512, 576, 672, 756, 768, 864, 896, 1008, 1152, 1344, 1512, 1536, 1728, 1792, 2016, 2304, 2688, 3024, 3456, 3584, 4032, 4608, 5376, 6048, 6912, 8064, 10752, 12096, 13824, 16128, 24192, 32256, 48384, 96768.
What is 96768 in binary?
10111101000000000 (hexadecimal 17A00, octal 275000).
What is the square root of 96768?
About 311.0756, exactly 48√42.
Is 96768 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 96768?
96768 is a Harshad number: divisible by its digit sum 36.