The number 33000
33000 is a composite number with 64 divisors. Its prime factorisation is × 3 × × 11. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 25, 30 … 33000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 33000: a Harshad number: divisible by its digit sum 6.
- 2
33000 is composite. Its prime factorisation is
- 3
The divisors add up to 112320; without 33000 itself that is 79320, so 33000 is abundant (79320 is more than 33000). Euler's totient φ(33000) = 8000 numbers up to 33000 share no factor with it.
- 4
The digits of 33000 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 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33000 = 2^{3} \times 3 \times 5^{3} \times 11 \]33000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 112320 |
| Euler totient φ(n) | 8000 |
| Square | 1089000000 |
| Cube | 35937000000000 |
| Square root | 181.659021 (= 10√330) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 41 |
| Scientific notation | 3.3 × |
33000 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand |
| Binary (base 2) | 1000000011101000 |
| Octal (base 8) | 100350 |
| Hexadecimal (base 16) | 80E8 |
| Base 3 | 1200021020 |
| As time | 33000 seconds = 9 h 10 min 0 s |
Is 33000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33000 ÷ 2 = 16500) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33000 ÷ 3 = 11000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33000 ÷ 4 = 8250) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (33000 ÷ 5 = 6600) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33000 ÷ 6 = 5500) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (33000 ÷ 8 = 4125) | 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 | Yes (33000 ÷ 10 = 3300) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (33000 ÷ 11 = 3000) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33000 ÷ 12 = 2750) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33000 a prime number?
No. 33000 = × 3 × × 11, so it is divisible by 2.
What are the factors of 33000?
1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 40, 44, 50, 55, 60, 66, 75, 88, 100, 110, 120, 125, 132, 150, 165, 200, 220, 250, 264, 275, 300, 330, 375, 440, 500, 550, 600, 660, 750, 825, 1000, 1100, 1320, 1375, 1500, 1650, 2200, 2750, 3000, 3300, 4125, 5500, 6600, 8250, 11000, 16500, 33000.
What is 33000 in binary?
1000000011101000 (hexadecimal 80E8, octal 100350).
What is the square root of 33000?
About 181.6590, exactly 10√330.
Is 33000 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 33000?
33000 is a Harshad number: divisible by its digit sum 6.