The number 33864
33864 is a composite number with 32 divisors. Its prime factorisation is × 3 × 17 × 83. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 83, 102, 136, 166 … 33864.
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How to work it out
- 1
What is special about 33864: a Harshad number: divisible by its digit sum 24.
- 2
33864 is composite. Its prime factorisation is
- 3
The divisors add up to 90720; without 33864 itself that is 56856, so 33864 is abundant (56856 is more than 33864). Euler's totient φ(33864) = 10496 numbers up to 33864 share no factor with it.
- 4
The digits of 33864 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 204 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33864 = 2^{3} \times 3 \times 17 \times 83 \]33864 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 90720 |
| Euler totient φ(n) | 10496 |
| Square | 1146770496 |
| Cube | 38834236076544 |
| Square root | 184.021738 (= 2√8466) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 204 |
| Scientific notation | 3.3864 × |
33864 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand eight hundred and sixty-four |
| Binary (base 2) | 1000010001001000 |
| Octal (base 8) | 102110 |
| Hexadecimal (base 16) | 8448 |
| Base 3 | 1201110020 |
| As time | 33864 seconds = 9 h 24 min 24 s |
Is 33864 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33864 ÷ 2 = 16932) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (33864 ÷ 3 = 11288) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (33864 ÷ 4 = 8466) | 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 (33864 ÷ 6 = 5644) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (33864 ÷ 8 = 4233) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (33864 ÷ 12 = 2822) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33864 a prime number?
No. 33864 = × 3 × 17 × 83, so it is divisible by 2.
What are the factors of 33864?
1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 83, 102, 136, 166, 204, 249, 332, 408, 498, 664, 996, 1411, 1992, 2822, 4233, 5644, 8466, 11288, 16932, 33864.
What is 33864 in binary?
1000010001001000 (hexadecimal 8448, octal 102110).
What is the square root of 33864?
About 184.0217, exactly 2√8466.
Is 33864 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 33864?
33864 is a Harshad number: divisible by its digit sum 24.