The number 333
333 is a palindrome: it reads 333 backwards too. Its prime factorisation is × 37. Divisors (6): 1, 3, 9, 37, 111, 333.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 333: a palindrome: it reads 333 backwards too; a Harshad number: divisible by its digit sum 9.
- 2
333 is composite. Its prime factorisation is
- 3
The divisors add up to 494; without 333 itself that is 161, so 333 is deficient (161 is less than 333). Euler's totient φ(333) = 216 numbers up to 333 share no factor with it.
- 4
The digits of 333 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 333 = 3^{2} \times 37 \]333 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 494 |
| Euler totient φ(n) | 216 |
| Square | 110889 |
| Cube | 36926037 |
| Square root | 18.248288 (= 3√37) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 112 |
| Scientific notation | 3.33 × |
333 in other forms
| Form | Value |
|---|---|
| In words | three hundred and thirty-three |
| Roman numerals | CCCXXXIII |
| Binary (base 2) | 101001101 |
| Octal (base 8) | 515 |
| Hexadecimal (base 16) | 14D |
| Base 3 | 110100 |
| As time | 333 seconds = 5 min 33 s |
Is 333 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 (333 ÷ 3 = 111) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 4) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (333 ÷ 9 = 37) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 333 a prime number?
No. 333 = × 37, so it is divisible by 3.
What are the factors of 333?
1, 3, 9, 37, 111, 333.
What is 333 in binary?
101001101 (hexadecimal 14D, octal 515).
What is the square root of 333?
About 18.2483, exactly 3√37.
What is 333 in Roman numerals?
CCCXXXIII.
Is 333 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 333?
333 is a palindrome: it reads 333 backwards too; a Harshad number: divisible by its digit sum 9.