The number 13013
13013 is a composite number with 12 divisors. Its prime factorisation is 7 × 11 × . Divisors (12): 1, 7, 11, 13, 77, 91, 143, 169, 1001, 1183, 1859, 13013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13013 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13013 is composite. Its prime factorisation is
- 3
The divisors add up to 17568; without 13013 itself that is 4555, so 13013 is deficient (4555 is less than 13013). Euler's totient φ(13013) = 9360 numbers up to 13013 share no factor with it.
- 4
The digits of 13013 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13013 = 7 \times 11 \times 13^{2} \]13013 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 17568 |
| Euler totient φ(n) | 9360 |
| Square | 169338169 |
| Cube | 2203597593197 |
| Square root | 114.074537 (= 13√77) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3013 × |
13013 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and thirteen |
| Binary (base 2) | 11001011010101 |
| Octal (base 8) | 31325 |
| Hexadecimal (base 16) | 32D5 |
| Base 3 | 122211222 |
| As time | 13013 seconds = 3 h 36 min 53 s |
Is 13013 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 | Yes (13013 ÷ 7 = 1859) | 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 8) | 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 | Yes (13013 ÷ 11 = 1183) | 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 13013 a prime number?
No. 13013 = 7 × 11 × , so it is divisible by 7.
What are the factors of 13013?
1, 7, 11, 13, 77, 91, 143, 169, 1001, 1183, 1859, 13013.
What is 13013 in binary?
11001011010101 (hexadecimal 32D5, octal 31325).
What is the square root of 13013?
About 114.0745, exactly 13√77.
Is 13013 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 13013?
It is a composite number with 12 divisors.