The number 8221
8221 is a twin prime (8219 and 8221 are both prime) and the 1031st prime number. Its only divisors are 1 and 8221.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8221: a twin prime (8219 and 8221 are both prime); the 1031st prime number.
- 2
8221 is prime, so its only factors are 1 and 8221. It is the 1031st prime; the next prime is 8231 and the one before is 8219.
- 3
The divisors add up to 8222; without 8221 itself that is 1, so 8221 is deficient (1 is less than 8221). Euler's totient φ(8221) = 8220 numbers up to 8221 share no factor with it.
- 4
The digits of 8221 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
8221 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 8222 |
| Euler totient φ(n) | 8220 |
| Square | 67584841 |
| Cube | 555614977861 |
| Square root | 90.669730 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 39 |
| Scientific notation | 8.221 × |
8221 in other forms
| Form | Value |
|---|---|
| In words | eight thousand two hundred and twenty-one |
| Binary (base 2) | 10000000011101 |
| Octal (base 8) | 20035 |
| Hexadecimal (base 16) | 201D |
| Base 3 | 102021111 |
| As time | 8221 seconds = 2 h 17 min 1 s |
Is 8221 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 | No (remainder 1) | 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 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | 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 | No (remainder 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8221 a prime number?
Yes. 8221 is divisible only by 1 and itself.
What are the factors of 8221?
1, 8221.
What is 8221 in binary?
10000000011101 (hexadecimal 201D, octal 20035).
What is the square root of 8221?
About 90.6697.
Is 8221 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 8221?
8221 is a twin prime (8219 and 8221 are both prime); the 1031st prime number.