The number 9728
9728 is a composite number with 20 divisors. Its prime factorisation is × 19. Divisors (20): 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608 … 9728.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9728 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9728 is composite. Its prime factorisation is
- 3
The divisors add up to 20460; without 9728 itself that is 10732, so 9728 is abundant (10732 is more than 9728). Euler's totient φ(9728) = 4608 numbers up to 9728 share no factor with it.
- 4
The digits of 9728 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9728 = 2^{9} \times 19 \]9728 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 20460 |
| Euler totient φ(n) | 4608 |
| Square | 94633984 |
| Cube | 920599396352 |
| Square root | 98.630624 (= 16√38) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 29 |
| Scientific notation | 9.728 × |
9728 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and twenty-eight |
| Binary (base 2) | 10011000000000 |
| Octal (base 8) | 23000 |
| Hexadecimal (base 16) | 2600 |
| Base 3 | 111100022 |
| As time | 9728 seconds = 2 h 42 min 8 s |
Is 9728 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9728 ÷ 2 = 4864) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9728 ÷ 4 = 2432) | 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 | No (remainder 2) | 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 (9728 ÷ 8 = 1216) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9728 a prime number?
No. 9728 = × 19, so it is divisible by 2.
What are the factors of 9728?
1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1216, 2432, 4864, 9728.
What is 9728 in binary?
10011000000000 (hexadecimal 2600, octal 23000).
What is the square root of 9728?
About 98.6306, exactly 16√38.
Is 9728 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 9728?
It is a composite number with 20 divisors.