The number 3003
3003 is a triangular number: 1 + 2 + … + 77 = 3003 and a palindrome: it reads 3003 backwards too. Its prime factorisation is 3 × 7 × 11 × 13. Divisors (16): 1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3003: a triangular number: 1 + 2 + … + 77 = 3003; a palindrome: it reads 3003 backwards too.
- 2
3003 is composite. Its prime factorisation is
- 3
The divisors add up to 5376; without 3003 itself that is 2373, so 3003 is deficient (2373 is less than 3003). Euler's totient φ(3003) = 1440 numbers up to 3003 share no factor with it.
- 4
The digits of 3003 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3003 = 3 \times 7 \times 11 \times 13 \]
3003 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 5376 |
| Euler totient φ(n) | 1440 |
| Square | 9018009 |
| Cube | 27081081027 |
| Square root | 54.799635 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 40 |
| Scientific notation | 3.003 × |
3003 in other forms
| Form | Value |
|---|---|
| In words | three thousand and three |
| Roman numerals | MMMIII |
| Binary (base 2) | 101110111011 |
| Octal (base 8) | 5673 |
| Hexadecimal (base 16) | BBB |
| Base 3 | 11010020 |
| As time | 3003 seconds = 50 min 3 s |
Is 3003 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 (3003 ÷ 3 = 1001) | 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 | Yes (3003 ÷ 7 = 429) | 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 | No (remainder 6) | 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 | Yes (3003 ÷ 11 = 273) | 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 3003 a prime number?
No. 3003 = 3 × 7 × 11 × 13, so it is divisible by 3.
What are the factors of 3003?
1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003.
What is 3003 in binary?
101110111011 (hexadecimal BBB, octal 5673).
What is the square root of 3003?
About 54.7996.
What is 3003 in Roman numerals?
MMMIII.
Is 3003 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 3003?
3003 is a triangular number: 1 + 2 + … + 77 = 3003; a palindrome: it reads 3003 backwards too.