The number 8204
8204 is a composite number with 12 divisors. Its prime factorisation is × 7 × 293. Divisors (12): 1, 2, 4, 7, 14, 28, 293, 586, 1172, 2051, 4102, 8204.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8204: a Harshad number: divisible by its digit sum 14.
- 2
8204 is composite. Its prime factorisation is
- 3
The divisors add up to 16464; without 8204 itself that is 8260, so 8204 is abundant (8260 is more than 8204). Euler's totient φ(8204) = 3504 numbers up to 8204 share no factor with it.
- 4
The digits of 8204 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8204 = 2^{2} \times 7 \times 293 \]8204 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 16464 |
| Euler totient φ(n) | 3504 |
| Square | 67305616 |
| Cube | 552175273664 |
| Square root | 90.575935 (= 2√2051) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 39 |
| Scientific notation | 8.204 × |
8204 in other forms
| Form | Value |
|---|---|
| In words | eight thousand two hundred and four |
| Binary (base 2) | 10000000001100 |
| Octal (base 8) | 20014 |
| Hexadecimal (base 16) | 200C |
| Base 3 | 102020212 |
| As time | 8204 seconds = 2 h 16 min 44 s |
Is 8204 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8204 ÷ 2 = 4102) | 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 (8204 ÷ 4 = 2051) | 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 (8204 ÷ 7 = 1172) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 9) | 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 8204 a prime number?
No. 8204 = × 7 × 293, so it is divisible by 2.
What are the factors of 8204?
1, 2, 4, 7, 14, 28, 293, 586, 1172, 2051, 4102, 8204.
What is 8204 in binary?
10000000001100 (hexadecimal 200C, octal 20014).
What is the square root of 8204?
About 90.5759, exactly 2√2051.
Is 8204 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 8204?
8204 is a Harshad number: divisible by its digit sum 14.