The number 999
999 is a palindrome: it reads 999 backwards too. Its prime factorisation is × 37. Divisors (8): 1, 3, 9, 27, 37, 111, 333, 999.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 999: a palindrome: it reads 999 backwards too; a Harshad number: divisible by its digit sum 27.
- 2
999 is composite. Its prime factorisation is
- 3
The divisors add up to 1520; without 999 itself that is 521, so 999 is deficient (521 is less than 999). Euler's totient φ(999) = 648 numbers up to 999 share no factor with it.
- 4
The digits of 999 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 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 999 = 3^{3} \times 37 \]999 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1520 |
| Euler totient φ(n) | 648 |
| Square | 998001 |
| Cube | 997002999 |
| Square root | 31.606961 (= 3√111) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 49 |
| Scientific notation | 9.99 × |
999 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and ninety-nine |
| Roman numerals | CMXCIX |
| Binary (base 2) | 1111100111 |
| Octal (base 8) | 1747 |
| Hexadecimal (base 16) | 3E7 |
| Base 3 | 1101000 |
| As time | 999 seconds = 16 min 39 s |
Is 999 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 (999 ÷ 3 = 333) | 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 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (999 ÷ 9 = 111) | 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 | No (remainder 9) | 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 999 a prime number?
No. 999 = × 37, so it is divisible by 3.
What are the factors of 999?
1, 3, 9, 27, 37, 111, 333, 999.
What is 999 in binary?
1111100111 (hexadecimal 3E7, octal 1747).
What is the square root of 999?
About 31.6070, exactly 3√111.
What is 999 in Roman numerals?
CMXCIX.
Is 999 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 999?
999 is a palindrome: it reads 999 backwards too; a Harshad number: divisible by its digit sum 27.