The number 10824
10824 is a composite number with 32 divisors. Its prime factorisation is × 3 × 11 × 41. Divisors (32): 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 41, 44, 66, 82, 88 … 10824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10824 is composite. Its prime factorisation is
- 3
The divisors add up to 30240; without 10824 itself that is 19416, so 10824 is abundant (19416 is more than 10824). Euler's totient φ(10824) = 3200 numbers up to 10824 share no factor with it.
- 4
The digits of 10824 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10824 = 2^{3} \times 3 \times 11 \times 41 \]10824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 30240 |
| Euler totient φ(n) | 3200 |
| Square | 117158976 |
| Cube | 1268128756224 |
| Square root | 104.038454 (= 2√2706) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.0824 × |
10824 in other forms
| Form | Value |
|---|---|
| In words | ten thousand eight hundred and twenty-four |
| Binary (base 2) | 10101001001000 |
| Octal (base 8) | 25110 |
| Hexadecimal (base 16) | 2A48 |
| Base 3 | 112211220 |
| As time | 10824 seconds = 3 h 0 min 24 s |
Is 10824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10824 ÷ 2 = 5412) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10824 ÷ 3 = 3608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10824 ÷ 4 = 2706) | 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 (10824 ÷ 6 = 1804) | 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 | Yes (10824 ÷ 8 = 1353) | 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 | Yes (10824 ÷ 11 = 984) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10824 ÷ 12 = 902) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10824 a prime number?
No. 10824 = × 3 × 11 × 41, so it is divisible by 2.
What are the factors of 10824?
1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 41, 44, 66, 82, 88, 123, 132, 164, 246, 264, 328, 451, 492, 902, 984, 1353, 1804, 2706, 3608, 5412, 10824.
What is 10824 in binary?
10101001001000 (hexadecimal 2A48, octal 25110).
What is the square root of 10824?
About 104.0385, exactly 2√2706.
Is 10824 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 10824?
It is a composite number with 32 divisors.