The number 2221
2221 is the 331st prime number. Its only divisors are 1 and 2221.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2221: the 331st prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
2221 is prime, so its only factors are 1 and 2221. It is the 331st prime; the next prime is 2237 and the one before is 2213.
- 3
The divisors add up to 2222; without 2221 itself that is 1, so 2221 is deficient (1 is less than 2221). Euler's totient φ(2221) = 2220 numbers up to 2221 share no factor with it.
- 4
The digits of 2221 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 32 steps to reach 1.
2221 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 2222 |
| Euler totient φ(n) | 2220 |
| Square | 4932841 |
| Cube | 10955839861 |
| Square root | 47.127487 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 32 |
| Scientific notation | 2.221 × |
2221 in other forms
| Form | Value |
|---|---|
| In words | two thousand two hundred and twenty-one |
| Roman numerals | MMCCXXI |
| Binary (base 2) | 100010101101 |
| Octal (base 8) | 4255 |
| Hexadecimal (base 16) | 8AD |
| Base 3 | 10001021 |
| As time | 2221 seconds = 37 min 1 s |
Is 2221 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 2) | 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 10) | 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 2221 a prime number?
Yes. 2221 is divisible only by 1 and itself.
What are the factors of 2221?
1, 2221.
What is 2221 in binary?
100010101101 (hexadecimal 8AD, octal 4255).
What is the square root of 2221?
About 47.1275.
What is 2221 in Roman numerals?
MMCCXXI.
Is 2221 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 2221?
2221 is the 331st prime number; a happy number: repeatedly adding the squares of its digits reaches 1.