The number 13184
13184 is a composite number with 16 divisors. Its prime factorisation is × 103. Divisors (16): 1, 2, 4, 8, 16, 32, 64, 103, 128, 206, 412, 824, 1648, 3296, 6592, 13184.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13184: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
13184 is composite. Its prime factorisation is
- 3
The divisors add up to 26520; without 13184 itself that is 13336, so 13184 is abundant (13336 is more than 13184). Euler's totient φ(13184) = 6528 numbers up to 13184 share no factor with it.
- 4
The digits of 13184 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13184 = 2^{7} \times 103 \]13184 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 26520 |
| Euler totient φ(n) | 6528 |
| Square | 173817856 |
| Cube | 2291614613504 |
| Square root | 114.821601 (= 8√206) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 94 |
| Scientific notation | 1.3184 × |
13184 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand one hundred and eighty-four |
| Binary (base 2) | 11001110000000 |
| Octal (base 8) | 31600 |
| Hexadecimal (base 16) | 3380 |
| Base 3 | 200002022 |
| As time | 13184 seconds = 3 h 39 min 44 s |
Is 13184 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13184 ÷ 2 = 6592) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13184 ÷ 4 = 3296) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (13184 ÷ 8 = 1648) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13184 a prime number?
No. 13184 = × 103, so it is divisible by 2.
What are the factors of 13184?
1, 2, 4, 8, 16, 32, 64, 103, 128, 206, 412, 824, 1648, 3296, 6592, 13184.
What is 13184 in binary?
11001110000000 (hexadecimal 3380, octal 31600).
What is the square root of 13184?
About 114.8216, exactly 8√206.
Is 13184 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 13184?
13184 is a happy number: repeatedly adding the squares of its digits reaches 1.