The number 2003
2003 is the 304th prime number. Its only divisors are 1 and 2003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2003: the 304th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
2003 is prime, so its only factors are 1 and 2003. It is the 304th prime; the next prime is 2011 and the one before is 1999.
- 3
The divisors add up to 2004; without 2003 itself that is 1, so 2003 is deficient (1 is less than 2003). Euler's totient φ(2003) = 2002 numbers up to 2003 share no factor with it.
- 4
The digits of 2003 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.
2003 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 2004 |
| Euler totient φ(n) | 2002 |
| Square | 4012009 |
| Cube | 8036054027 |
| Square root | 44.754888 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 143 |
| Scientific notation | 2.003 × |
2003 in other forms
| Form | Value |
|---|---|
| In words | two thousand and three |
| Roman numerals | MMIII |
| Binary (base 2) | 11111010011 |
| Octal (base 8) | 3723 |
| Hexadecimal (base 16) | 7D3 |
| Base 3 | 2202012 |
| As time | 2003 seconds = 33 min 23 s |
Is 2003 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 | No (remainder 2) | 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 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 5) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2003 a prime number?
Yes. 2003 is divisible only by 1 and itself.
What are the factors of 2003?
1, 2003.
What is 2003 in binary?
11111010011 (hexadecimal 7D3, octal 3723).
What is the square root of 2003?
About 44.7549.
What is 2003 in Roman numerals?
MMIII.
Is 2003 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 2003?
2003 is the 304th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.