The number 33824
33824 is a composite number with 24 divisors. Its prime factorisation is × 7 × 151. Divisors (24): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 151, 224, 302, 604, 1057 … 33824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
33824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
33824 is composite. Its prime factorisation is
- 3
The divisors add up to 76608; without 33824 itself that is 42784, so 33824 is abundant (42784 is more than 33824). Euler's totient φ(33824) = 14400 numbers up to 33824 share no factor with it.
- 4
The digits of 33824 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 85 steps to reach 1.
LaTeX source of the formulas on this page
\[ 33824 = 2^{5} \times 7 \times 151 \]33824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 76608 |
| Euler totient φ(n) | 14400 |
| Square | 1144062976 |
| Cube | 38696786100224 |
| Square root | 183.913023 (= 4√2114) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 85 |
| Scientific notation | 3.3824 × |
33824 in other forms
| Form | Value |
|---|---|
| In words | thirty-three thousand eight hundred and twenty-four |
| Binary (base 2) | 1000010000100000 |
| Octal (base 8) | 102040 |
| Hexadecimal (base 16) | 8420 |
| Base 3 | 1201101202 |
| As time | 33824 seconds = 9 h 23 min 44 s |
Is 33824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (33824 ÷ 2 = 16912) | 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 (33824 ÷ 4 = 8456) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (33824 ÷ 7 = 4832) | 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 (33824 ÷ 8 = 4228) | 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 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 33824 a prime number?
No. 33824 = × 7 × 151, so it is divisible by 2.
What are the factors of 33824?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 151, 224, 302, 604, 1057, 1208, 2114, 2416, 4228, 4832, 8456, 16912, 33824.
What is 33824 in binary?
1000010000100000 (hexadecimal 8420, octal 102040).
What is the square root of 33824?
About 183.9130, exactly 4√2114.
Is 33824 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 33824?
It is a composite number with 24 divisors.