The number 9504
9504 is a composite number with 48 divisors. Its prime factorisation is × × 11. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 32, 33 … 9504.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9504: a Harshad number: divisible by its digit sum 18.
- 2
9504 is composite. Its prime factorisation is
- 3
The divisors add up to 30240; without 9504 itself that is 20736, so 9504 is abundant (20736 is more than 9504). Euler's totient φ(9504) = 2880 numbers up to 9504 share no factor with it.
- 4
The digits of 9504 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 78 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9504 = 2^{5} \times 3^{3} \times 11 \]9504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 30240 |
| Euler totient φ(n) | 2880 |
| Square | 90326016 |
| Cube | 858458456064 |
| Square root | 97.488461 (= 12√66) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 78 |
| Scientific notation | 9.504 × |
9504 in other forms
| Form | Value |
|---|---|
| In words | nine thousand five hundred and four |
| Binary (base 2) | 10010100100000 |
| Octal (base 8) | 22440 |
| Hexadecimal (base 16) | 2520 |
| Base 3 | 111001000 |
| As time | 9504 seconds = 2 h 38 min 24 s |
Is 9504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9504 ÷ 2 = 4752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9504 ÷ 3 = 3168) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9504 ÷ 4 = 2376) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9504 ÷ 6 = 1584) | 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 (9504 ÷ 8 = 1188) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9504 ÷ 9 = 1056) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (9504 ÷ 11 = 864) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9504 ÷ 12 = 792) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9504 a prime number?
No. 9504 = × × 11, so it is divisible by 2.
What are the factors of 9504?
1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 32, 33, 36, 44, 48, 54, 66, 72, 88, 96, 99, 108, 132, 144, 176, 198, 216, 264, 288, 297, 352, 396, 432, 528, 594, 792, 864, 1056, 1188, 1584, 2376, 3168, 4752, 9504.
What is 9504 in binary?
10010100100000 (hexadecimal 2520, octal 22440).
What is the square root of 9504?
About 97.4885, exactly 12√66.
Is 9504 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 9504?
9504 is a Harshad number: divisible by its digit sum 18.