The number 9768
9768 is a composite number with 32 divisors. Its prime factorisation is × 3 × 11 × 37. Divisors (32): 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 37, 44, 66, 74, 88 … 9768.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9768: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
9768 is composite. Its prime factorisation is
- 3
The divisors add up to 27360; without 9768 itself that is 17592, so 9768 is abundant (17592 is more than 9768). Euler's totient φ(9768) = 2880 numbers up to 9768 share no factor with it.
- 4
The digits of 9768 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9768 = 2^{3} \times 3 \times 11 \times 37 \]9768 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 27360 |
| Euler totient φ(n) | 2880 |
| Square | 95413824 |
| Cube | 932002232832 |
| Square root | 98.833193 (= 2√2442) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 42 |
| Scientific notation | 9.768 × |
9768 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and sixty-eight |
| Binary (base 2) | 10011000101000 |
| Octal (base 8) | 23050 |
| Hexadecimal (base 16) | 2628 |
| Base 3 | 111101210 |
| As time | 9768 seconds = 2 h 42 min 48 s |
Is 9768 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9768 ÷ 2 = 4884) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9768 ÷ 3 = 3256) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9768 ÷ 4 = 2442) | 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 (9768 ÷ 6 = 1628) | 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 (9768 ÷ 8 = 1221) | 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 | Yes (9768 ÷ 11 = 888) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9768 ÷ 12 = 814) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9768 a prime number?
No. 9768 = × 3 × 11 × 37, so it is divisible by 2.
What are the factors of 9768?
1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 37, 44, 66, 74, 88, 111, 132, 148, 222, 264, 296, 407, 444, 814, 888, 1221, 1628, 2442, 3256, 4884, 9768.
What is 9768 in binary?
10011000101000 (hexadecimal 2628, octal 23050).
What is the square root of 9768?
About 98.8332, exactly 2√2442.
Is 9768 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 9768?
9768 is a happy number: repeatedly adding the squares of its digits reaches 1.