The number 6003
6003 is a composite number with 12 divisors. Its prime factorisation is × 23 × 29. Divisors (12): 1, 3, 9, 23, 29, 69, 87, 207, 261, 667, 2001, 6003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6003: a Harshad number: divisible by its digit sum 9.
- 2
6003 is composite. Its prime factorisation is
- 3
The divisors add up to 9360; without 6003 itself that is 3357, so 6003 is deficient (3357 is less than 6003). Euler's totient φ(6003) = 3696 numbers up to 6003 share no factor with it.
- 4
The digits of 6003 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 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 6003 = 3^{2} \times 23 \times 29 \]6003 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 9360 |
| Euler totient φ(n) | 3696 |
| Square | 36036009 |
| Cube | 216324162027 |
| Square root | 77.479029 (= 3√667) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 41 |
| Scientific notation | 6.003 × |
6003 in other forms
| Form | Value |
|---|---|
| In words | six thousand and three |
| Binary (base 2) | 1011101110011 |
| Octal (base 8) | 13563 |
| Hexadecimal (base 16) | 1773 |
| Base 3 | 22020100 |
| As time | 6003 seconds = 1 h 40 min 3 s |
Is 6003 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 (6003 ÷ 3 = 2001) | 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 | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (6003 ÷ 9 = 667) | 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 8) | 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 6003 a prime number?
No. 6003 = × 23 × 29, so it is divisible by 3.
What are the factors of 6003?
1, 3, 9, 23, 29, 69, 87, 207, 261, 667, 2001, 6003.
What is 6003 in binary?
1011101110011 (hexadecimal 1773, octal 13563).
What is the square root of 6003?
About 77.4790, exactly 3√667.
Is 6003 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 6003?
6003 is a Harshad number: divisible by its digit sum 9.