The number 33984
33984 is a composite number with 42 divisors. Its prime factorisation is × × 59. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 59, 64 … 33984.
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How to work it out
- 1
33984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33984 is composite. Its prime factorisation is
- 3
The divisors add up to 99060; without 33984 itself that is 65076, so 33984 is abundant (65076 is more than 33984). Euler's totient φ(33984) = 11136 numbers up to 33984 share no factor with it.
- 4
The digits of 33984 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33984 = 2^{6} \times 3^{2} \times 59 \]33984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 99060 |
| Euler totient φ(n) | 11136 |
| Square | 1154912256 |
| Cube | 39248538107904 |
| Square root | 184.347498 (= 24√59) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 129 |
| Scientific notation | 3.3984 × |
33984 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and eighty-four |
| Binary (base 2) | 1000010011000000 |
| Octal (base 8) | 102300 |
| Hexadecimal (base 16) | 84C0 |
| Base 3 | 1201121200 |
| As time | 33984 seconds = 9 h 26 min 24 s |
Is 33984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33984 ÷ 2 = 16992) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33984 ÷ 3 = 11328) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33984 ÷ 4 = 8496) | 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 (33984 ÷ 6 = 5664) | 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 | Yes (33984 ÷ 8 = 4248) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33984 ÷ 9 = 3776) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33984 ÷ 12 = 2832) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33984 a prime number?
No. 33984 = × × 59, so it is divisible by 2.
What are the factors of 33984?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 59, 64, 72, 96, 118, 144, 177, 192, 236, 288, 354, 472, 531, 576, 708, 944, 1062, 1416, 1888, 2124, 2832, 3776, 4248, 5664, 8496, 11328, 16992, 33984.
What is 33984 in binary?
1000010011000000 (hexadecimal 84C0, octal 102300).
What is the square root of 33984?
About 184.3475, exactly 24√59.
Is 33984 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 33984?
It is a composite number with 42 divisors.