The number 9600
9600 is a composite number with 48 divisors. Its prime factorisation is × 3 × . Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32 … 9600.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9600: a Harshad number: divisible by its digit sum 15.
- 2
9600 is composite. Its prime factorisation is
- 3
The divisors add up to 31620; without 9600 itself that is 22020, so 9600 is abundant (22020 is more than 9600). Euler's totient φ(9600) = 2560 numbers up to 9600 share no factor with it.
- 4
The digits of 9600 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 21 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9600 = 2^{7} \times 3 \times 5^{2} \]9600 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 31620 |
| Euler totient φ(n) | 2560 |
| Square | 92160000 |
| Cube | 884736000000 |
| Square root | 97.979590 (= 40√6) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 21 |
| Scientific notation | 9.6 × |
9600 in other forms
| Form | Value |
|---|---|
| In words | nine thousand six hundred |
| Binary (base 2) | 10010110000000 |
| Octal (base 8) | 22600 |
| Hexadecimal (base 16) | 2580 |
| Base 3 | 111011120 |
| As time | 9600 seconds = 2 h 40 min 0 s |
Is 9600 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9600 ÷ 2 = 4800) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9600 ÷ 3 = 3200) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9600 ÷ 4 = 2400) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9600 ÷ 5 = 1920) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9600 ÷ 6 = 1600) | 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 (9600 ÷ 8 = 1200) | 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 | Yes (9600 ÷ 10 = 960) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9600 ÷ 12 = 800) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9600 a prime number?
No. 9600 = × 3 × , so it is divisible by 2.
What are the factors of 9600?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600.
What is 9600 in binary?
10010110000000 (hexadecimal 2580, octal 22600).
What is the square root of 9600?
About 97.9796, exactly 40√6.
Is 9600 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 9600?
9600 is a Harshad number: divisible by its digit sum 15.