The number 8200
8200 is a composite number with 24 divisors. Its prime factorisation is × × 41. Divisors (24): 1, 2, 4, 5, 8, 10, 20, 25, 40, 41, 50, 82, 100, 164, 200, 205 … 8200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8200: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
8200 is composite. Its prime factorisation is
- 3
The divisors add up to 19530; without 8200 itself that is 11330, so 8200 is abundant (11330 is more than 8200). Euler's totient φ(8200) = 3200 numbers up to 8200 share no factor with it.
- 4
The digits of 8200 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8200 = 2^{3} \times 5^{2} \times 41 \]8200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 19530 |
| Euler totient φ(n) | 3200 |
| Square | 67240000 |
| Cube | 551368000000 |
| Square root | 90.553851 (= 10√82) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 39 |
| Scientific notation | 8.2 × |
8200 in other forms
| Form | Value |
|---|---|
| In words | eight thousand two hundred |
| Binary (base 2) | 10000000001000 |
| Octal (base 8) | 20010 |
| Hexadecimal (base 16) | 2008 |
| Base 3 | 102020201 |
| As time | 8200 seconds = 2 h 16 min 40 s |
Is 8200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8200 ÷ 2 = 4100) | 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 (8200 ÷ 4 = 2050) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (8200 ÷ 5 = 1640) | 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 3) | 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 (8200 ÷ 8 = 1025) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (8200 ÷ 10 = 820) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | 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 8200 a prime number?
No. 8200 = × × 41, so it is divisible by 2.
What are the factors of 8200?
1, 2, 4, 5, 8, 10, 20, 25, 40, 41, 50, 82, 100, 164, 200, 205, 328, 410, 820, 1025, 1640, 2050, 4100, 8200.
What is 8200 in binary?
10000000001000 (hexadecimal 2008, octal 20010).
What is the square root of 8200?
About 90.5539, exactly 10√82.
Is 8200 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 8200?
8200 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.