The number 13185
13185 is a composite number with 12 divisors. Its prime factorisation is × 5 × 293. Divisors (12): 1, 3, 5, 9, 15, 45, 293, 879, 1465, 2637, 4395, 13185.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13185: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13185 is composite. Its prime factorisation is
- 3
The divisors add up to 22932; without 13185 itself that is 9747, so 13185 is deficient (9747 is less than 13185). Euler's totient φ(13185) = 7008 numbers up to 13185 share no factor with it.
- 4
The digits of 13185 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13185 = 3^{2} \times 5 \times 293 \]13185 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 22932 |
| Euler totient φ(n) | 7008 |
| Square | 173844225 |
| Cube | 2292136106625 |
| Square root | 114.825955 (= 3√1465) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 125 |
| Scientific notation | 1.3185 × |
13185 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand one hundred and eighty-five |
| Binary (base 2) | 11001110000001 |
| Octal (base 8) | 31601 |
| Hexadecimal (base 16) | 3381 |
| Base 3 | 200002100 |
| As time | 13185 seconds = 3 h 39 min 45 s |
Is 13185 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 (13185 ÷ 3 = 4395) | 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 (13185 ÷ 5 = 2637) | 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 4) | 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 | Yes (13185 ÷ 9 = 1465) | 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 7) | 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 13185 a prime number?
No. 13185 = × 5 × 293, so it is divisible by 3.
What are the factors of 13185?
1, 3, 5, 9, 15, 45, 293, 879, 1465, 2637, 4395, 13185.
What is 13185 in binary?
11001110000001 (hexadecimal 3381, octal 31601).
What is the square root of 13185?
About 114.8260, exactly 3√1465.
Is 13185 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13185?
13185 is a happy number: repeatedly adding the squares of its digits reaches 1.