The number 21824
21824 is a composite number with 28 divisors. Its prime factorisation is × 11 × 31. Divisors (28): 1, 2, 4, 8, 11, 16, 22, 31, 32, 44, 62, 64, 88, 124, 176, 248 … 21824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
21824 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
21824 is composite. Its prime factorisation is
- 3
The divisors add up to 48768; without 21824 itself that is 26944, so 21824 is abundant (26944 is more than 21824). Euler's totient φ(21824) = 9600 numbers up to 21824 share no factor with it.
- 4
The digits of 21824 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 17 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21824 = 2^{6} \times 11 \times 31 \]21824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 48768 |
| Euler totient φ(n) | 9600 |
| Square | 476286976 |
| Cube | 10394486964224 |
| Square root | 147.729483 (= 8√341) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 17 |
| Scientific notation | 2.1824 × |
21824 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand eight hundred and twenty-four |
| Binary (base 2) | 101010101000000 |
| Octal (base 8) | 52500 |
| Hexadecimal (base 16) | 5540 |
| Base 3 | 1002221022 |
| As time | 21824 seconds = 6 h 3 min 44 s |
Is 21824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21824 ÷ 2 = 10912) | 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 (21824 ÷ 4 = 5456) | 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 | 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 (21824 ÷ 8 = 2728) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 (21824 ÷ 11 = 1984) | 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 21824 a prime number?
No. 21824 = × 11 × 31, so it is divisible by 2.
What are the factors of 21824?
1, 2, 4, 8, 11, 16, 22, 31, 32, 44, 62, 64, 88, 124, 176, 248, 341, 352, 496, 682, 704, 992, 1364, 1984, 2728, 5456, 10912, 21824.
What is 21824 in binary?
101010101000000 (hexadecimal 5540, octal 52500).
What is the square root of 21824?
About 147.7295, exactly 8√341.
Is 21824 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 21824?
It is a composite number with 28 divisors.