The number 8217
8217 is a composite number with 12 divisors. Its prime factorisation is × 11 × 83. Divisors (12): 1, 3, 9, 11, 33, 83, 99, 249, 747, 913, 2739, 8217.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
8217 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
8217 is composite. Its prime factorisation is
- 3
The divisors add up to 13104; without 8217 itself that is 4887, so 8217 is deficient (4887 is less than 8217). Euler's totient φ(8217) = 4920 numbers up to 8217 share no factor with it.
- 4
The digits of 8217 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 158 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8217 = 3^{2} \times 11 \times 83 \]8217 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 13104 |
| Euler totient φ(n) | 4920 |
| Square | 67519089 |
| Cube | 554804354313 |
| Square root | 90.647670 (= 3√913) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 158 |
| Scientific notation | 8.217 × |
8217 in other forms
| Form | Value |
|---|---|
| In words | eight thousand two hundred and seventeen |
| Binary (base 2) | 10000000011001 |
| Octal (base 8) | 20031 |
| Hexadecimal (base 16) | 2019 |
| Base 3 | 102021100 |
| As time | 8217 seconds = 2 h 16 min 57 s |
Is 8217 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8217 ÷ 3 = 2739) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (8217 ÷ 9 = 913) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (8217 ÷ 11 = 747) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8217 a prime number?
No. 8217 = × 11 × 83, so it is divisible by 3.
What are the factors of 8217?
1, 3, 9, 11, 33, 83, 99, 249, 747, 913, 2739, 8217.
What is 8217 in binary?
10000000011001 (hexadecimal 2019, octal 20031).
What is the square root of 8217?
About 90.6477, exactly 3√913.
Is 8217 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 8217?
It is a composite number with 12 divisors.