The number 9999
9999 is a palindrome: it reads 9999 backwards too. Its prime factorisation is × 11 × 101. Divisors (12): 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333, 9999.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9999: a palindrome: it reads 9999 backwards too.
- 2
9999 is composite. Its prime factorisation is
- 3
The divisors add up to 15912; without 9999 itself that is 5913, so 9999 is deficient (5913 is less than 9999). Euler's totient φ(9999) = 6000 numbers up to 9999 share no factor with it.
- 4
The digits of 9999 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 91 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9999 = 3^{2} \times 11 \times 101 \]9999 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 15912 |
| Euler totient φ(n) | 6000 |
| Square | 99980001 |
| Cube | 999700029999 |
| Square root | 99.995000 (= 3√1111) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 91 |
| Scientific notation | 9.999 × |
9999 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and ninety-nine |
| Binary (base 2) | 10011100001111 |
| Octal (base 8) | 23417 |
| Hexadecimal (base 16) | 270F |
| Base 3 | 111201100 |
| As time | 9999 seconds = 2 h 46 min 39 s |
Is 9999 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 (9999 ÷ 3 = 3333) | 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 4) | 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 3) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9999 ÷ 9 = 1111) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (9999 ÷ 11 = 909) | 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 9999 a prime number?
No. 9999 = × 11 × 101, so it is divisible by 3.
What are the factors of 9999?
1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333, 9999.
What is 9999 in binary?
10011100001111 (hexadecimal 270F, octal 23417).
What is the square root of 9999?
About 99.9950, exactly 3√1111.
Is 9999 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 9999?
9999 is a palindrome: it reads 9999 backwards too.