The number 33003
33003 is a composite number with 12 divisors. Its prime factorisation is × 19 × 193. Divisors (12): 1, 3, 9, 19, 57, 171, 193, 579, 1737, 3667, 11001, 33003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33003: a Harshad number: divisible by its digit sum 9.
- 2
33003 is composite. Its prime factorisation is
- 3
The divisors add up to 50440; without 33003 itself that is 17437, so 33003 is deficient (17437 is less than 33003). Euler's totient φ(33003) = 20736 numbers up to 33003 share no factor with it.
- 4
The digits of 33003 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 72 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33003 = 3^{2} \times 19 \times 193 \]33003 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 50440 |
| Euler totient φ(n) | 20736 |
| Square | 1089198009 |
| Cube | 35946801891027 |
| Square root | 181.667278 (= 3√3667) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 72 |
| Scientific notation | 3.3003 × |
33003 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand and three |
| Binary (base 2) | 1000000011101011 |
| Octal (base 8) | 100353 |
| Hexadecimal (base 16) | 80EB |
| Base 3 | 1200021100 |
| As time | 33003 seconds = 9 h 10 min 3 s |
Is 33003 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 (33003 ÷ 3 = 11001) | 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 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33003 ÷ 9 = 3667) | 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 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33003 a prime number?
No. 33003 = × 19 × 193, so it is divisible by 3.
What are the factors of 33003?
1, 3, 9, 19, 57, 171, 193, 579, 1737, 3667, 11001, 33003.
What is 33003 in binary?
1000000011101011 (hexadecimal 80EB, octal 100353).
What is the square root of 33003?
About 181.6673, exactly 3√3667.
Is 33003 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 33003?
33003 is a Harshad number: divisible by its digit sum 9.