The number 9648
9648 is a composite number with 30 divisors. Its prime factorisation is × × 67. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 67, 72, 134 … 9648.
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How to work it out
- 1
9648 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9648 is composite. Its prime factorisation is
- 3
The divisors add up to 27404; without 9648 itself that is 17756, so 9648 is abundant (17756 is more than 9648). Euler's totient φ(9648) = 3168 numbers up to 9648 share no factor with it.
- 4
The digits of 9648 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 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9648 = 2^{4} \times 3^{2} \times 67 \]9648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 27404 |
| Euler totient φ(n) | 3168 |
| Square | 93083904 |
| Cube | 898073505792 |
| Square root | 98.224233 (= 12√67) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.648 × |
9648 in other forms
| Form | Value |
|---|---|
| In words | nine thousand six hundred and forty-eight |
| Binary (base 2) | 10010110110000 |
| Octal (base 8) | 22660 |
| Hexadecimal (base 16) | 25B0 |
| Base 3 | 111020100 |
| As time | 9648 seconds = 2 h 40 min 48 s |
Is 9648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9648 ÷ 2 = 4824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9648 ÷ 3 = 3216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9648 ÷ 4 = 2412) | 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 (9648 ÷ 6 = 1608) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (9648 ÷ 8 = 1206) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9648 ÷ 9 = 1072) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9648 ÷ 12 = 804) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9648 a prime number?
No. 9648 = × × 67, so it is divisible by 2.
What are the factors of 9648?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 67, 72, 134, 144, 201, 268, 402, 536, 603, 804, 1072, 1206, 1608, 2412, 3216, 4824, 9648.
What is 9648 in binary?
10010110110000 (hexadecimal 25B0, octal 22660).
What is the square root of 9648?
About 98.2242, exactly 12√67.
Is 9648 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9648?
It is a composite number with 30 divisors.