The number 33968
33968 is a composite number with 20 divisors. Its prime factorisation is × 11 × 193. Divisors (20): 1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 193, 386, 772, 1544, 2123, 3088 … 33968.
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How to work it out
- 1
33968 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33968 is composite. Its prime factorisation is
- 3
The divisors add up to 72168; without 33968 itself that is 38200, so 33968 is abundant (38200 is more than 33968). Euler's totient φ(33968) = 15360 numbers up to 33968 share no factor with it.
- 4
The digits of 33968 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33968 = 2^{4} \times 11 \times 193 \]33968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 72168 |
| Euler totient φ(n) | 15360 |
| Square | 1153825024 |
| Cube | 39193128415232 |
| Square root | 184.304097 (= 4√2123) |
| Digit sum / digital root | 29 / 2 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.3968 × |
33968 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and sixty-eight |
| Binary (base 2) | 1000010010110000 |
| Octal (base 8) | 102260 |
| Hexadecimal (base 16) | 84B0 |
| Base 3 | 1201121002 |
| As time | 33968 seconds = 9 h 26 min 8 s |
Is 33968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33968 ÷ 2 = 16984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33968 ÷ 4 = 8492) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (33968 ÷ 8 = 4246) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (33968 ÷ 11 = 3088) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33968 a prime number?
No. 33968 = × 11 × 193, so it is divisible by 2.
What are the factors of 33968?
1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 193, 386, 772, 1544, 2123, 3088, 4246, 8492, 16984, 33968.
What is 33968 in binary?
1000010010110000 (hexadecimal 84B0, octal 102260).
What is the square root of 33968?
About 184.3041, exactly 4√2123.
Is 33968 divisible by 3?
No. Its digits add up to 29, which is not a multiple of 3.
What is special about the number 33968?
It is a composite number with 20 divisors.