The number 12084
12084 is a composite number with 24 divisors. Its prime factorisation is × 3 × 19 × 53. Divisors (24): 1, 2, 3, 4, 6, 12, 19, 38, 53, 57, 76, 106, 114, 159, 212, 228 … 12084.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
12084 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
12084 is composite. Its prime factorisation is
- 3
The divisors add up to 30240; without 12084 itself that is 18156, so 12084 is abundant (18156 is more than 12084). Euler's totient φ(12084) = 3744 numbers up to 12084 share no factor with it.
- 4
The digits of 12084 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12084 = 2^{2} \times 3 \times 19 \times 53 \]12084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 30240 |
| Euler totient φ(n) | 3744 |
| Square | 146023056 |
| Cube | 1764542608704 |
| Square root | 109.927249 (= 2√3021) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 68 |
| Scientific notation | 1.2084 × |
12084 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand and eighty-four |
| Binary (base 2) | 10111100110100 |
| Octal (base 8) | 27464 |
| Hexadecimal (base 16) | 2F34 |
| Base 3 | 121120120 |
| As time | 12084 seconds = 3 h 21 min 24 s |
Is 12084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12084 ÷ 2 = 6042) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12084 ÷ 3 = 4028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12084 ÷ 4 = 3021) | 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 (12084 ÷ 6 = 2014) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | No (remainder 6) | 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 | Yes (12084 ÷ 12 = 1007) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12084 a prime number?
No. 12084 = × 3 × 19 × 53, so it is divisible by 2.
What are the factors of 12084?
1, 2, 3, 4, 6, 12, 19, 38, 53, 57, 76, 106, 114, 159, 212, 228, 318, 636, 1007, 2014, 3021, 4028, 6042, 12084.
What is 12084 in binary?
10111100110100 (hexadecimal 2F34, octal 27464).
What is the square root of 12084?
About 109.9272, exactly 2√3021.
Is 12084 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 12084?
It is a composite number with 24 divisors.