The number 9660
9660 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 7 × 23. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 28, 30 … 9660.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9660: a Harshad number: divisible by its digit sum 21.
- 2
9660 is composite. Its prime factorisation is
- 3
The divisors add up to 32256; without 9660 itself that is 22596, so 9660 is abundant (22596 is more than 9660). Euler's totient φ(9660) = 2112 numbers up to 9660 share no factor with it.
- 4
The digits of 9660 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 122 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9660 = 2^{2} \times 3 \times 5 \times 7 \times 23 \]9660 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 32256 |
| Euler totient φ(n) | 2112 |
| Square | 93315600 |
| Cube | 901428696000 |
| Square root | 98.285299 (= 2√2415) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 122 |
| Scientific notation | 9.66 × |
9660 in other forms
| Form | Value |
|---|---|
| In words | nine thousand six hundred and sixty |
| Binary (base 2) | 10010110111100 |
| Octal (base 8) | 22674 |
| Hexadecimal (base 16) | 25BC |
| Base 3 | 111020210 |
| As time | 9660 seconds = 2 h 41 min 0 s |
Is 9660 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9660 ÷ 2 = 4830) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9660 ÷ 3 = 3220) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9660 ÷ 4 = 2415) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9660 ÷ 5 = 1932) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9660 ÷ 6 = 1610) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (9660 ÷ 7 = 1380) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9660 ÷ 10 = 966) | 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 (9660 ÷ 12 = 805) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9660 a prime number?
No. 9660 = × 3 × 5 × 7 × 23, so it is divisible by 2.
What are the factors of 9660?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 28, 30, 35, 42, 46, 60, 69, 70, 84, 92, 105, 115, 138, 140, 161, 210, 230, 276, 322, 345, 420, 460, 483, 644, 690, 805, 966, 1380, 1610, 1932, 2415, 3220, 4830, 9660.
What is 9660 in binary?
10010110111100 (hexadecimal 25BC, octal 22674).
What is the square root of 9660?
About 98.2853, exactly 2√2415.
Is 9660 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 9660?
9660 is a Harshad number: divisible by its digit sum 21.