The number 8208
8208 is an Armstrong number: each digit raised to the power 4 adds up to 8208. Its prime factorisation is × × 19. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 36, 38, 48 … 8208.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8208: an Armstrong number: each digit raised to the power 4 adds up to 8208; a Harshad number: divisible by its digit sum 18.
- 2
8208 is composite. Its prime factorisation is
- 3
The divisors add up to 24800; without 8208 itself that is 16592, so 8208 is abundant (16592 is more than 8208). Euler's totient φ(8208) = 2592 numbers up to 8208 share no factor with it.
- 4
The digits of 8208 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8208 = 2^{4} \times 3^{3} \times 19 \]8208 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 24800 |
| Euler totient φ(n) | 2592 |
| Square | 67371264 |
| Cube | 552983334912 |
| Square root | 90.598013 (= 12√57) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 39 |
| Scientific notation | 8.208 × |
8208 in other forms
| Form | Value |
|---|---|
| In words | eight thousand two hundred and eight |
| Binary (base 2) | 10000000010000 |
| Octal (base 8) | 20020 |
| Hexadecimal (base 16) | 2010 |
| Base 3 | 102021000 |
| As time | 8208 seconds = 2 h 16 min 48 s |
Is 8208 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8208 ÷ 2 = 4104) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8208 ÷ 3 = 2736) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8208 ÷ 4 = 2052) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8208 ÷ 6 = 1368) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (8208 ÷ 8 = 1026) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (8208 ÷ 9 = 912) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8208 ÷ 12 = 684) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8208 a prime number?
No. 8208 = × × 19, so it is divisible by 2.
What are the factors of 8208?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 36, 38, 48, 54, 57, 72, 76, 108, 114, 144, 152, 171, 216, 228, 304, 342, 432, 456, 513, 684, 912, 1026, 1368, 2052, 2736, 4104, 8208.
What is 8208 in binary?
10000000010000 (hexadecimal 2010, octal 20020).
What is the square root of 8208?
About 90.5980, exactly 12√57.
Is 8208 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 8208?
8208 is an Armstrong number: each digit raised to the power 4 adds up to 8208; a Harshad number: divisible by its digit sum 18.