The number 13523
13523 is the 1602nd prime number. Its only divisors are 1 and 13523.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13523: the 1602nd prime number.
- 2
13523 is prime, so its only factors are 1 and 13523. It is the 1602nd prime; the next prime is 13537 and the one before is 13513.
- 3
The divisors add up to 13524; without 13523 itself that is 1, so 13523 is deficient (1 is less than 13523). Euler's totient φ(13523) = 13522 numbers up to 13523 share no factor with it.
- 4
The digits of 13523 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
13523 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13524 |
| Euler totient φ(n) | 13522 |
| Square | 182871529 |
| Cube | 2472971686667 |
| Square root | 116.288435 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 89 |
| Scientific notation | 1.3523 × |
13523 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and twenty-three |
| Binary (base 2) | 11010011010011 |
| Octal (base 8) | 32323 |
| Hexadecimal (base 16) | 34D3 |
| Base 3 | 200112212 |
| As time | 13523 seconds = 3 h 45 min 23 s |
Is 13523 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 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 5) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13523 a prime number?
Yes. 13523 is divisible only by 1 and itself.
What are the factors of 13523?
1, 13523.
What is 13523 in binary?
11010011010011 (hexadecimal 34D3, octal 32323).
What is the square root of 13523?
About 116.2884.
Is 13523 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 13523?
13523 is the 1602nd prime number.