The number 10513
10513 is the 1286th prime number. Its only divisors are 1 and 10513.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10513: the 1286th prime number.
- 2
10513 is prime, so its only factors are 1 and 10513. It is the 1286th prime; the next prime is 10529 and the one before is 10501.
- 3
The divisors add up to 10514; without 10513 itself that is 1, so 10513 is deficient (1 is less than 10513). Euler's totient φ(10513) = 10512 numbers up to 10513 share no factor with it.
- 4
The digits of 10513 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 29 steps to reach 1.
10513 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 10514 |
| Euler totient φ(n) | 10512 |
| Square | 110523169 |
| Cube | 1161930075697 |
| Square root | 102.532922 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.0513 × |
10513 in other forms
| Form | Value |
|---|---|
| In words | ten thousand five hundred and thirteen |
| Binary (base 2) | 10100100010001 |
| Octal (base 8) | 24421 |
| Hexadecimal (base 16) | 2911 |
| Base 3 | 112102101 |
| As time | 10513 seconds = 2 h 55 min 13 s |
Is 10513 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 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 1) | 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 8) | 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 10513 a prime number?
Yes. 10513 is divisible only by 1 and itself.
What are the factors of 10513?
1, 10513.
What is 10513 in binary?
10100100010001 (hexadecimal 2911, octal 24421).
What is the square root of 10513?
About 102.5329.
Is 10513 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 10513?
10513 is the 1286th prime number.