The number 13005
13005 is a composite number with 18 divisors. Its prime factorisation is × 5 × . Divisors (18): 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 289, 765, 867, 1445, 2601 … 13005.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13005: a Harshad number: divisible by its digit sum 9.
- 2
13005 is composite. Its prime factorisation is
- 3
The divisors add up to 23946; without 13005 itself that is 10941, so 13005 is deficient (10941 is less than 13005). Euler's totient φ(13005) = 6528 numbers up to 13005 share no factor with it.
- 4
The digits of 13005 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13005 = 3^{2} \times 5 \times 17^{2} \]13005 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 23946 |
| Euler totient φ(n) | 6528 |
| Square | 169130025 |
| Cube | 2199535975125 |
| Square root | 114.039467 (= 51√5) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.3005 × |
13005 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand and five |
| Binary (base 2) | 11001011001101 |
| Octal (base 8) | 31315 |
| Hexadecimal (base 16) | 32CD |
| Base 3 | 122211200 |
| As time | 13005 seconds = 3 h 36 min 45 s |
Is 13005 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 | Yes (13005 ÷ 3 = 4335) | 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 | Yes (13005 ÷ 5 = 2601) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13005 ÷ 9 = 1445) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13005 a prime number?
No. 13005 = × 5 × , so it is divisible by 3.
What are the factors of 13005?
1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 289, 765, 867, 1445, 2601, 4335, 13005.
What is 13005 in binary?
11001011001101 (hexadecimal 32CD, octal 31315).
What is the square root of 13005?
About 114.0395, exactly 51√5.
Is 13005 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 13005?
13005 is a Harshad number: divisible by its digit sum 9.