The number 33966
33966 is a composite number with 32 divisors. Its prime factorisation is 2 × × 17 × 37. Divisors (32): 1, 2, 3, 6, 9, 17, 18, 27, 34, 37, 51, 54, 74, 102, 111, 153 … 33966.
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How to work it out
- 1
What is special about 33966: a Harshad number: divisible by its digit sum 27.
- 2
33966 is composite. Its prime factorisation is
- 3
The divisors add up to 82080; without 33966 itself that is 48114, so 33966 is abundant (48114 is more than 33966). Euler's totient φ(33966) = 10368 numbers up to 33966 share no factor with it.
- 4
The digits of 33966 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 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33966 = 2 \times 3^{3} \times 17 \times 37 \]33966 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 82080 |
| Euler totient φ(n) | 10368 |
| Square | 1153689156 |
| Cube | 39186205872696 |
| Square root | 184.298671 (= 3√3774) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 111 |
| Scientific notation | 3.3966 × |
33966 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand nine hundred and sixty-six |
| Binary (base 2) | 1000010010101110 |
| Octal (base 8) | 102256 |
| Hexadecimal (base 16) | 84AE |
| Base 3 | 1201121000 |
| As time | 33966 seconds = 9 h 26 min 6 s |
Is 33966 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33966 ÷ 2 = 16983) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33966 ÷ 3 = 11322) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (33966 ÷ 6 = 5661) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (33966 ÷ 9 = 3774) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33966 a prime number?
No. 33966 = 2 × × 17 × 37, so it is divisible by 2.
What are the factors of 33966?
1, 2, 3, 6, 9, 17, 18, 27, 34, 37, 51, 54, 74, 102, 111, 153, 222, 306, 333, 459, 629, 666, 918, 999, 1258, 1887, 1998, 3774, 5661, 11322, 16983, 33966.
What is 33966 in binary?
1000010010101110 (hexadecimal 84AE, octal 102256).
What is the square root of 33966?
About 184.2987, exactly 3√3774.
Is 33966 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 33966?
33966 is a Harshad number: divisible by its digit sum 27.