The number 83221
83221 is a twin prime (83219 and 83221 are both prime) and the 8124th prime number. Its only divisors are 1 and 83221.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83221: a twin prime (83219 and 83221 are both prime); the 8124th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83221 is prime, so its only factors are 1 and 83221. It is the 8124th prime; the next prime is 83227 and the one before is 83219.
- 3
The divisors add up to 83222; without 83221 itself that is 1, so 83221 is deficient (1 is less than 83221). Euler's totient φ(83221) = 83220 numbers up to 83221 share no factor with it.
- 4
The digits of 83221 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
83221 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 83222 |
| Euler totient φ(n) | 83220 |
| Square | 6925734841 |
| Cube | 576366579202861 |
| Square root | 288.480502 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.3221 × |
83221 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand two hundred and twenty-one |
| Binary (base 2) | 10100010100010101 |
| Octal (base 8) | 242425 |
| Hexadecimal (base 16) | 14515 |
| Base 3 | 11020011021 |
| As time | 83221 seconds = 23 h 7 min 1 s |
Is 83221 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 5) | 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 7) | 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 6) | 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 83221 a prime number?
Yes. 83221 is divisible only by 1 and itself.
What are the factors of 83221?
1, 83221.
What is 83221 in binary?
10100010100010101 (hexadecimal 14515, octal 242425).
What is the square root of 83221?
About 288.4805.
Is 83221 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 83221?
83221 is a twin prime (83219 and 83221 are both prime); the 8124th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.