The number 13509
13509 is a composite number with 12 divisors. Its prime factorisation is × 19 × 79. Divisors (12): 1, 3, 9, 19, 57, 79, 171, 237, 711, 1501, 4503, 13509.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13509 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13509 is composite. Its prime factorisation is
- 3
The divisors add up to 20800; without 13509 itself that is 7291, so 13509 is deficient (7291 is less than 13509). Euler's totient φ(13509) = 8424 numbers up to 13509 share no factor with it.
- 4
The digits of 13509 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13509 = 3^{2} \times 19 \times 79 \]13509 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 20800 |
| Euler totient φ(n) | 8424 |
| Square | 182493081 |
| Cube | 2465299031229 |
| Square root | 116.228224 (= 3√1501) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 37 |
| Scientific notation | 1.3509 × |
13509 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and nine |
| Binary (base 2) | 11010011000101 |
| Octal (base 8) | 32305 |
| Hexadecimal (base 16) | 34C5 |
| Base 3 | 200112100 |
| As time | 13509 seconds = 3 h 45 min 9 s |
Is 13509 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 (13509 ÷ 3 = 4503) | 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 4) | 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 (13509 ÷ 9 = 1501) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 13509 a prime number?
No. 13509 = × 19 × 79, so it is divisible by 3.
What are the factors of 13509?
1, 3, 9, 19, 57, 79, 171, 237, 711, 1501, 4503, 13509.
What is 13509 in binary?
11010011000101 (hexadecimal 34C5, octal 32305).
What is the square root of 13509?
About 116.2282, exactly 3√1501.
Is 13509 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13509?
It is a composite number with 12 divisors.