The number 10013
10013 is a composite number with 8 divisors. Its prime factorisation is 17 × 19 × 31. Divisors (8): 1, 17, 19, 31, 323, 527, 589, 10013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
10013 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
10013 is composite. Its prime factorisation is
- 3
The divisors add up to 11520; without 10013 itself that is 1507, so 10013 is deficient (1507 is less than 10013). Euler's totient φ(10013) = 8640 numbers up to 10013 share no factor with it.
- 4
The digits of 10013 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10013 = 17 \times 19 \times 31 \]
10013 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 11520 |
| Euler totient φ(n) | 8640 |
| Square | 100260169 |
| Cube | 1003905072197 |
| Square root | 100.064979 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 65 |
| Scientific notation | 1.0013 × |
10013 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and thirteen |
| Binary (base 2) | 10011100011101 |
| Octal (base 8) | 23435 |
| Hexadecimal (base 16) | 271D |
| Base 3 | 111201212 |
| As time | 10013 seconds = 2 h 46 min 53 s |
Is 10013 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 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 5) | 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 3) | 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 10013 a prime number?
No. 10013 = 17 × 19 × 31, so it is divisible by 17.
What are the factors of 10013?
1, 17, 19, 31, 323, 527, 589, 10013.
What is 10013 in binary?
10011100011101 (hexadecimal 271D, octal 23435).
What is the square root of 10013?
About 100.0650.
Is 10013 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 10013?
It is a composite number with 8 divisors.