The number 13104
13104 is a composite number with 60 divisors. Its prime factorisation is × × 7 × 13. Divisors (60): 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 21, 24, 26 … 13104.
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How to work it out
- 1
What is special about 13104: a Harshad number: divisible by its digit sum 9.
- 2
13104 is composite. Its prime factorisation is
- 3
The divisors add up to 45136; without 13104 itself that is 32032, so 13104 is abundant (32032 is more than 13104). Euler's totient φ(13104) = 3456 numbers up to 13104 share no factor with it.
- 4
The digits of 13104 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 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13104 = 2^{4} \times 3^{2} \times 7 \times 13 \]13104 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 45136 |
| Euler totient φ(n) | 3456 |
| Square | 171714816 |
| Cube | 2250150948864 |
| Square root | 114.472704 (= 12√91) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 45 |
| Scientific notation | 1.3104 × |
13104 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand one hundred and four |
| Binary (base 2) | 11001100110000 |
| Octal (base 8) | 31460 |
| Hexadecimal (base 16) | 3330 |
| Base 3 | 122222100 |
| As time | 13104 seconds = 3 h 38 min 24 s |
Is 13104 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13104 ÷ 2 = 6552) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13104 ÷ 3 = 4368) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13104 ÷ 4 = 3276) | 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 | Yes (13104 ÷ 6 = 2184) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (13104 ÷ 7 = 1872) | 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 (13104 ÷ 8 = 1638) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13104 ÷ 9 = 1456) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (13104 ÷ 12 = 1092) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13104 a prime number?
No. 13104 = × × 7 × 13, so it is divisible by 2.
What are the factors of 13104?
1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 21, 24, 26, 28, 36, 39, 42, 48, 52, 56, 63, 72, 78, 84, 91, 104, 112, 117, 126, 144, 156, 168, 182, 208, 234, 252, 273, 312, 336, 364, 468, 504, 546, 624, 728, 819, 936, 1008, 1092, 1456, 1638, 1872, 2184, 3276, 4368, 6552, 13104.
What is 13104 in binary?
11001100110000 (hexadecimal 3330, octal 31460).
What is the square root of 13104?
About 114.4727, exactly 12√91.
Is 13104 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 13104?
13104 is a Harshad number: divisible by its digit sum 9.