The number 9792
9792 is a composite number with 42 divisors. Its prime factorisation is × × 17. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48 … 9792.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9792 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9792 is composite. Its prime factorisation is
- 3
The divisors add up to 29718; without 9792 itself that is 19926, so 9792 is abundant (19926 is more than 9792). Euler's totient φ(9792) = 3072 numbers up to 9792 share no factor with it.
- 4
The digits of 9792 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9792 = 2^{6} \times 3^{2} \times 17 \]9792 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 29718 |
| Euler totient φ(n) | 3072 |
| Square | 95883264 |
| Cube | 938888921088 |
| Square root | 98.954535 (= 24√17) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 9.792 × |
9792 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and ninety-two |
| Binary (base 2) | 10011001000000 |
| Octal (base 8) | 23100 |
| Hexadecimal (base 16) | 2640 |
| Base 3 | 111102200 |
| As time | 9792 seconds = 2 h 43 min 12 s |
Is 9792 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9792 ÷ 2 = 4896) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9792 ÷ 3 = 3264) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9792 ÷ 4 = 2448) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9792 ÷ 6 = 1632) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (9792 ÷ 8 = 1224) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9792 ÷ 9 = 1088) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9792 ÷ 12 = 816) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9792 a prime number?
No. 9792 = × × 17, so it is divisible by 2.
What are the factors of 9792?
1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48, 51, 64, 68, 72, 96, 102, 136, 144, 153, 192, 204, 272, 288, 306, 408, 544, 576, 612, 816, 1088, 1224, 1632, 2448, 3264, 4896, 9792.
What is 9792 in binary?
10011001000000 (hexadecimal 2640, octal 23100).
What is the square root of 9792?
About 98.9545, exactly 24√17.
Is 9792 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9792?
It is a composite number with 42 divisors.