The number 2213
2213 is the 330th prime number. Its only divisors are 1 and 2213.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2213: the 330th prime number.
- 2
2213 is prime, so its only factors are 1 and 2213. It is the 330th prime; the next prime is 2221 and the one before is 2207.
- 3
The divisors add up to 2214; without 2213 itself that is 1, so 2213 is deficient (1 is less than 2213). Euler's totient φ(2213) = 2212 numbers up to 2213 share no factor with it.
- 4
The digits of 2213 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
2213 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 2214 |
| Euler totient φ(n) | 2212 |
| Square | 4897369 |
| Cube | 10837877597 |
| Square root | 47.042534 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 138 |
| Scientific notation | 2.213 × |
2213 in other forms
| Form | Value |
|---|---|
| In words | two thousand two hundred and thirteen |
| Roman numerals | MMCCXIII |
| Binary (base 2) | 100010100101 |
| Octal (base 8) | 4245 |
| Hexadecimal (base 16) | 8A5 |
| Base 3 | 10000222 |
| As time | 2213 seconds = 36 min 53 s |
Is 2213 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 2) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | 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 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2213 a prime number?
Yes. 2213 is divisible only by 1 and itself.
What are the factors of 2213?
1, 2213.
What is 2213 in binary?
100010100101 (hexadecimal 8A5, octal 4245).
What is the square root of 2213?
About 47.0425.
What is 2213 in Roman numerals?
MMCCXIII.
Is 2213 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 2213?
2213 is the 330th prime number.