The number 8224
8224 is a composite number with 12 divisors. Its prime factorisation is × 257. Divisors (12): 1, 2, 4, 8, 16, 32, 257, 514, 1028, 2056, 4112, 8224.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8224: a Harshad number: divisible by its digit sum 16.
- 2
8224 is composite. Its prime factorisation is
- 3
The divisors add up to 16254; without 8224 itself that is 8030, so 8224 is deficient (8030 is less than 8224). Euler's totient φ(8224) = 4096 numbers up to 8224 share no factor with it.
- 4
The digits of 8224 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 127 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8224 = 2^{5} \times 257 \]8224 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 16254 |
| Euler totient φ(n) | 4096 |
| Square | 67634176 |
| Cube | 556223463424 |
| Square root | 90.686272 (= 4√514) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 127 |
| Scientific notation | 8.224 × |
8224 in other forms
| Form | Value |
|---|---|
| In words | eight thousand two hundred and twenty-four |
| Binary (base 2) | 10000000100000 |
| Octal (base 8) | 20040 |
| Hexadecimal (base 16) | 2020 |
| Base 3 | 102021121 |
| As time | 8224 seconds = 2 h 17 min 4 s |
Is 8224 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8224 ÷ 2 = 4112) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8224 ÷ 4 = 2056) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (8224 ÷ 8 = 1028) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8224 a prime number?
No. 8224 = × 257, so it is divisible by 2.
What are the factors of 8224?
1, 2, 4, 8, 16, 32, 257, 514, 1028, 2056, 4112, 8224.
What is 8224 in binary?
10000000100000 (hexadecimal 2020, octal 20040).
What is the square root of 8224?
About 90.6863, exactly 4√514.
Is 8224 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 8224?
8224 is a Harshad number: divisible by its digit sum 16.