The number 223
223 is the 48th prime number. Its only divisors are 1 and 223.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 223: the 48th prime number.
- 2
223 is prime, so its only factors are 1 and 223. It is the 48th prime; the next prime is 227 and the one before is 211.
- 3
The divisors add up to 224; without 223 itself that is 1, so 223 is deficient (1 is less than 223). Euler's totient φ(223) = 222 numbers up to 223 share no factor with it.
- 4
The digits of 223 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 70 steps to reach 1.
223 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 224 |
| Euler totient φ(n) | 222 |
| Square | 49729 |
| Cube | 11089567 |
| Square root | 14.933185 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 70 |
| Scientific notation | 2.23 × |
223 in other forms
| Form | Value |
|---|---|
| In words | two hundred and twenty-three |
| Roman numerals | CCXXIII |
| Binary (base 2) | 11011111 |
| Octal (base 8) | 337 |
| Hexadecimal (base 16) | DF |
| Base 3 | 22021 |
| As time | 223 seconds = 3 min 43 s |
Is 223 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 3) | 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 1) | 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 7) | 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 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 223 a prime number?
Yes. 223 is divisible only by 1 and itself.
What are the factors of 223?
1, 223.
What is 223 in binary?
11011111 (hexadecimal DF, octal 337).
What is the square root of 223?
About 14.9332.
What is 223 in Roman numerals?
CCXXIII.
Is 223 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 223?
223 is the 48th prime number.