The number 33084
33084 is a composite number with 18 divisors. Its prime factorisation is × × 919. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 919, 1838, 2757, 3676, 5514, 8271, 11028 … 33084.
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How to work it out
- 1
What is special about 33084: a Harshad number: divisible by its digit sum 18.
- 2
33084 is composite. Its prime factorisation is
- 3
The divisors add up to 83720; without 33084 itself that is 50636, so 33084 is abundant (50636 is more than 33084). Euler's totient φ(33084) = 11016 numbers up to 33084 share no factor with it.
- 4
The digits of 33084 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33084 = 2^{2} \times 3^{2} \times 919 \]33084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 83720 |
| Euler totient φ(n) | 11016 |
| Square | 1094551056 |
| Cube | 36212127136704 |
| Square root | 181.890077 (= 6√919) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 98 |
| Scientific notation | 3.3084 × |
33084 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand and eighty-four |
| Binary (base 2) | 1000000100111100 |
| Octal (base 8) | 100474 |
| Hexadecimal (base 16) | 813C |
| Base 3 | 1200101100 |
| As time | 33084 seconds = 9 h 11 min 24 s |
Is 33084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33084 ÷ 2 = 16542) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33084 ÷ 3 = 11028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33084 ÷ 4 = 8271) | 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 | Yes (33084 ÷ 6 = 5514) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33084 ÷ 9 = 3676) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33084 ÷ 12 = 2757) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33084 a prime number?
No. 33084 = × × 919, so it is divisible by 2.
What are the factors of 33084?
1, 2, 3, 4, 6, 9, 12, 18, 36, 919, 1838, 2757, 3676, 5514, 8271, 11028, 16542, 33084.
What is 33084 in binary?
1000000100111100 (hexadecimal 813C, octal 100474).
What is the square root of 33084?
About 181.8901, exactly 6√919.
Is 33084 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 33084?
33084 is a Harshad number: divisible by its digit sum 18.