The number 13513
13513 is the 1601st prime number. Its only divisors are 1 and 13513.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13513: the 1601st prime number.
- 2
13513 is prime, so its only factors are 1 and 13513. It is the 1601st prime; the next prime is 13523 and the one before is 13499.
- 3
The divisors add up to 13514; without 13513 itself that is 1, so 13513 is deficient (1 is less than 13513). Euler's totient φ(13513) = 13512 numbers up to 13513 share no factor with it.
- 4
The digits of 13513 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
13513 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 13514 |
| Euler totient φ(n) | 13512 |
| Square | 182601169 |
| Cube | 2467489596697 |
| Square root | 116.245430 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.3513 × |
13513 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and thirteen |
| Binary (base 2) | 11010011001001 |
| Octal (base 8) | 32311 |
| Hexadecimal (base 16) | 34C9 |
| Base 3 | 200112111 |
| As time | 13513 seconds = 3 h 45 min 13 s |
Is 13513 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 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 4) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13513 a prime number?
Yes. 13513 is divisible only by 1 and itself.
What are the factors of 13513?
1, 13513.
What is 13513 in binary?
11010011001001 (hexadecimal 34C9, octal 32311).
What is the square root of 13513?
About 116.2454.
Is 13513 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 13513?
13513 is the 1601st prime number.