The number 9963
9963 is a composite number with 12 divisors. Its prime factorisation is × 41. Divisors (12): 1, 3, 9, 27, 41, 81, 123, 243, 369, 1107, 3321, 9963.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9963: a Harshad number: divisible by its digit sum 27.
- 2
9963 is composite. Its prime factorisation is
- 3
The divisors add up to 15288; without 9963 itself that is 5325, so 9963 is deficient (5325 is less than 9963). Euler's totient φ(9963) = 6480 numbers up to 9963 share no factor with it.
- 4
The digits of 9963 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
\[ 9963 = 3^{5} \times 41 \]9963 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 15288 |
| Euler totient φ(n) | 6480 |
| Square | 99261369 |
| Cube | 988941019347 |
| Square root | 99.814829 (= 9√123) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.963 × |
9963 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and sixty-three |
| Binary (base 2) | 10011011101011 |
| Octal (base 8) | 23353 |
| Hexadecimal (base 16) | 26EB |
| Base 3 | 111200000 |
| As time | 9963 seconds = 2 h 46 min 3 s |
Is 9963 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9963 ÷ 3 = 3321) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 | No (remainder 3) | 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 | No (remainder 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9963 ÷ 9 = 1107) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9963 a prime number?
No. 9963 = × 41, so it is divisible by 3.
What are the factors of 9963?
1, 3, 9, 27, 41, 81, 123, 243, 369, 1107, 3321, 9963.
What is 9963 in binary?
10011011101011 (hexadecimal 26EB, octal 23353).
What is the square root of 9963?
About 99.8148, exactly 9√123.
Is 9963 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9963?
9963 is a Harshad number: divisible by its digit sum 27.