The number 9996
9996 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 17. Divisors (36): 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 49, 51, 68 … 9996.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9996 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9996 is composite. Its prime factorisation is
- 3
The divisors add up to 28728; without 9996 itself that is 18732, so 9996 is abundant (18732 is more than 9996). Euler's totient φ(9996) = 2688 numbers up to 9996 share no factor with it.
- 4
The digits of 9996 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 179 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9996 = 2^{2} \times 3 \times 7^{2} \times 17 \]9996 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 28728 |
| Euler totient φ(n) | 2688 |
| Square | 99920016 |
| Cube | 998800479936 |
| Square root | 99.979998 (= 14√51) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 179 |
| Scientific notation | 9.996 × |
9996 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and ninety-six |
| Binary (base 2) | 10011100001100 |
| Octal (base 8) | 23414 |
| Hexadecimal (base 16) | 270C |
| Base 3 | 111201020 |
| As time | 9996 seconds = 2 h 46 min 36 s |
Is 9996 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9996 ÷ 2 = 4998) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9996 ÷ 3 = 3332) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9996 ÷ 4 = 2499) | 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 (9996 ÷ 6 = 1666) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (9996 ÷ 7 = 1428) | 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 6) | 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 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9996 ÷ 12 = 833) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9996 a prime number?
No. 9996 = × 3 × × 17, so it is divisible by 2.
What are the factors of 9996?
1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 49, 51, 68, 84, 98, 102, 119, 147, 196, 204, 238, 294, 357, 476, 588, 714, 833, 1428, 1666, 2499, 3332, 4998, 9996.
What is 9996 in binary?
10011100001100 (hexadecimal 270C, octal 23414).
What is the square root of 9996?
About 99.9800, exactly 14√51.
Is 9996 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 9996?
It is a composite number with 36 divisors.