The number 33384
33384 is a composite number with 32 divisors. Its prime factorisation is × 3 × 13 × 107. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 107, 156 … 33384.
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How to work it out
- 1
33384 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33384 is composite. Its prime factorisation is
- 3
The divisors add up to 90720; without 33384 itself that is 57336, so 33384 is abundant (57336 is more than 33384). Euler's totient φ(33384) = 10176 numbers up to 33384 share no factor with it.
- 4
The digits of 33384 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33384 = 2^{3} \times 3 \times 13 \times 107 \]33384 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 90720 |
| Euler totient φ(n) | 10176 |
| Square | 1114491456 |
| Cube | 37206182767104 |
| Square root | 182.712890 (= 2√8346) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.3384 × |
33384 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand three hundred and eighty-four |
| Binary (base 2) | 1000001001101000 |
| Octal (base 8) | 101150 |
| Hexadecimal (base 16) | 8268 |
| Base 3 | 1200210110 |
| As time | 33384 seconds = 9 h 16 min 24 s |
Is 33384 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33384 ÷ 2 = 16692) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33384 ÷ 3 = 11128) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33384 ÷ 4 = 8346) | 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 (33384 ÷ 6 = 5564) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (33384 ÷ 8 = 4173) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33384 ÷ 12 = 2782) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33384 a prime number?
No. 33384 = × 3 × 13 × 107, so it is divisible by 2.
What are the factors of 33384?
1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 107, 156, 214, 312, 321, 428, 642, 856, 1284, 1391, 2568, 2782, 4173, 5564, 8346, 11128, 16692, 33384.
What is 33384 in binary?
1000001001101000 (hexadecimal 8268, octal 101150).
What is the square root of 33384?
About 182.7129, exactly 2√8346.
Is 33384 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 33384?
It is a composite number with 32 divisors.