The number 13504
13504 is a composite number with 14 divisors. Its prime factorisation is × 211. Divisors (14): 1, 2, 4, 8, 16, 32, 64, 211, 422, 844, 1688, 3376, 6752, 13504.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
13504 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
13504 is composite. Its prime factorisation is
- 3
The divisors add up to 26924; without 13504 itself that is 13420, so 13504 is deficient (13420 is less than 13504). Euler's totient φ(13504) = 6720 numbers up to 13504 share no factor with it.
- 4
The digits of 13504 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13504 = 2^{6} \times 211 \]13504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 26924 |
| Euler totient φ(n) | 6720 |
| Square | 182358016 |
| Cube | 2462562648064 |
| Square root | 116.206712 (= 8√211) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3504 × |
13504 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand five hundred and four |
| Binary (base 2) | 11010011000000 |
| Octal (base 8) | 32300 |
| Hexadecimal (base 16) | 34C0 |
| Base 3 | 200112011 |
| As time | 13504 seconds = 3 h 45 min 4 s |
Is 13504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13504 ÷ 2 = 6752) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13504 ÷ 4 = 3376) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | Yes (13504 ÷ 8 = 1688) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13504 a prime number?
No. 13504 = × 211, so it is divisible by 2.
What are the factors of 13504?
1, 2, 4, 8, 16, 32, 64, 211, 422, 844, 1688, 3376, 6752, 13504.
What is 13504 in binary?
11010011000000 (hexadecimal 34C0, octal 32300).
What is the square root of 13504?
About 116.2067, exactly 8√211.
Is 13504 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 13504?
It is a composite number with 14 divisors.