The number 9966
9966 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 11 × 151. Divisors (16): 1, 2, 3, 6, 11, 22, 33, 66, 151, 302, 453, 906, 1661, 3322, 4983, 9966.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9966 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9966 is composite. Its prime factorisation is
- 3
The divisors add up to 21888; without 9966 itself that is 11922, so 9966 is abundant (11922 is more than 9966). Euler's totient φ(9966) = 3000 numbers up to 9966 share no factor with it.
- 4
The digits of 9966 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9966 = 2 \times 3 \times 11 \times 151 \]
9966 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 21888 |
| Euler totient φ(n) | 3000 |
| Square | 99321156 |
| Cube | 989834640696 |
| Square root | 99.829855 |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 104 |
| Scientific notation | 9.966 × |
9966 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and sixty-six |
| Binary (base 2) | 10011011101110 |
| Octal (base 8) | 23356 |
| Hexadecimal (base 16) | 26EE |
| Base 3 | 111200010 |
| As time | 9966 seconds = 2 h 46 min 6 s |
Is 9966 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9966 ÷ 2 = 4983) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9966 ÷ 3 = 3322) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9966 ÷ 6 = 1661) | 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 | No (remainder 6) | 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 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (9966 ÷ 11 = 906) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9966 a prime number?
No. 9966 = 2 × 3 × 11 × 151, so it is divisible by 2.
What are the factors of 9966?
1, 2, 3, 6, 11, 22, 33, 66, 151, 302, 453, 906, 1661, 3322, 4983, 9966.
What is 9966 in binary?
10011011101110 (hexadecimal 26EE, octal 23356).
What is the square root of 9966?
About 99.8299.
Is 9966 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 9966?
It is a composite number with 16 divisors.