The number 33004
33004 is a composite number with 12 divisors. Its prime factorisation is × 37 × 223. Divisors (12): 1, 2, 4, 37, 74, 148, 223, 446, 892, 8251, 16502, 33004.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
33004 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33004 is composite. Its prime factorisation is
- 3
The divisors add up to 59584; without 33004 itself that is 26580, so 33004 is deficient (26580 is less than 33004). Euler's totient φ(33004) = 15984 numbers up to 33004 share no factor with it.
- 4
The digits of 33004 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33004 = 2^{2} \times 37 \times 223 \]33004 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 59584 |
| Euler totient φ(n) | 15984 |
| Square | 1089264016 |
| Cube | 35950069584064 |
| Square root | 181.670031 (= 2√8251) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 67 |
| Scientific notation | 3.3004 × |
33004 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand and four |
| Binary (base 2) | 1000000011101100 |
| Octal (base 8) | 100354 |
| Hexadecimal (base 16) | 80EC |
| Base 3 | 1200021101 |
| As time | 33004 seconds = 9 h 10 min 4 s |
Is 33004 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33004 ÷ 2 = 16502) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33004 ÷ 4 = 8251) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33004 a prime number?
No. 33004 = × 37 × 223, so it is divisible by 2.
What are the factors of 33004?
1, 2, 4, 37, 74, 148, 223, 446, 892, 8251, 16502, 33004.
What is 33004 in binary?
1000000011101100 (hexadecimal 80EC, octal 100354).
What is the square root of 33004?
About 181.6700, exactly 2√8251.
Is 33004 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 33004?
It is a composite number with 12 divisors.