The number 13284
13284 is a composite number with 30 divisors. Its prime factorisation is × × 41. Divisors (30): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 41, 54, 81, 82, 108, 123 … 13284.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13284: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
13284 is composite. Its prime factorisation is
- 3
The divisors add up to 35574; without 13284 itself that is 22290, so 13284 is abundant (22290 is more than 13284). Euler's totient φ(13284) = 4320 numbers up to 13284 share no factor with it.
- 4
The digits of 13284 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 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13284 = 2^{2} \times 3^{4} \times 41 \]13284 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 35574 |
| Euler totient φ(n) | 4320 |
| Square | 176464656 |
| Cube | 2344156490304 |
| Square root | 115.256236 (= 18√41) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.3284 × |
13284 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand two hundred and eighty-four |
| Binary (base 2) | 11001111100100 |
| Octal (base 8) | 31744 |
| Hexadecimal (base 16) | 33E4 |
| Base 3 | 200020000 |
| As time | 13284 seconds = 3 h 41 min 24 s |
Is 13284 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13284 ÷ 2 = 6642) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (13284 ÷ 3 = 4428) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13284 ÷ 4 = 3321) | 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 (13284 ÷ 6 = 2214) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (13284 ÷ 9 = 1476) | 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 | Yes (13284 ÷ 12 = 1107) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13284 a prime number?
No. 13284 = × × 41, so it is divisible by 2.
What are the factors of 13284?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 41, 54, 81, 82, 108, 123, 162, 164, 246, 324, 369, 492, 738, 1107, 1476, 2214, 3321, 4428, 6642, 13284.
What is 13284 in binary?
11001111100100 (hexadecimal 33E4, octal 31744).
What is the square root of 13284?
About 115.2562, exactly 18√41.
Is 13284 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 13284?
13284 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.