The number 523
523 is a twin prime (521 and 523 are both prime) and the 99th prime number. Its only divisors are 1 and 523.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 523: a twin prime (521 and 523 are both prime); the 99th prime number.
- 2
523 is prime, so its only factors are 1 and 523. It is the 99th prime; the next prime is 541 and the one before is 521.
- 3
The divisors add up to 524; without 523 itself that is 1, so 523 is deficient (1 is less than 523). Euler's totient φ(523) = 522 numbers up to 523 share no factor with it.
- 4
The digits of 523 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 123 steps to reach 1.
523 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 524 |
| Euler totient φ(n) | 522 |
| Square | 273529 |
| Cube | 143055667 |
| Square root | 22.869193 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 123 |
| Scientific notation | 5.23 × |
523 in other forms
| Form | Value |
|---|---|
| In words | five hundred and twenty-three |
| Roman numerals | DXXIII |
| Binary (base 2) | 1000001011 |
| Octal (base 8) | 1013 |
| Hexadecimal (base 16) | 20B |
| Base 3 | 201101 |
| As time | 523 seconds = 8 min 43 s |
Is 523 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 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 6) | 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 523 a prime number?
Yes. 523 is divisible only by 1 and itself.
What are the factors of 523?
1, 523.
What is 523 in binary?
1000001011 (hexadecimal 20B, octal 1013).
What is the square root of 523?
About 22.8692.
What is 523 in Roman numerals?
DXXIII.
Is 523 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 523?
523 is a twin prime (521 and 523 are both prime); the 99th prime number.