The number 593
593 is the 108th prime number. Its only divisors are 1 and 593.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 593: the 108th prime number.
- 2
593 is prime, so its only factors are 1 and 593. It is the 108th prime; the next prime is 599 and the one before is 587.
- 3
The divisors add up to 594; without 593 itself that is 1, so 593 is deficient (1 is less than 593). Euler's totient φ(593) = 592 numbers up to 593 share no factor with it.
- 4
The digits of 593 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 74 steps to reach 1.
593 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 594 |
| Euler totient φ(n) | 592 |
| Square | 351649 |
| Cube | 208527857 |
| Square root | 24.351591 |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 74 |
| Scientific notation | 5.93 × |
593 in other forms
| Form | Value |
|---|---|
| In words | five hundred and ninety-three |
| Roman numerals | DXCIII |
| Binary (base 2) | 1001010001 |
| Octal (base 8) | 1121 |
| Hexadecimal (base 16) | 251 |
| Base 3 | 210222 |
| As time | 593 seconds = 9 min 53 s |
Is 593 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 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 1) | 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 10) | 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 593 a prime number?
Yes. 593 is divisible only by 1 and itself.
What are the factors of 593?
1, 593.
What is 593 in binary?
1001010001 (hexadecimal 251, octal 1121).
What is the square root of 593?
About 24.3516.
What is 593 in Roman numerals?
DXCIII.
Is 593 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 593?
593 is the 108th prime number.