The number 2184
2184 is a composite number with 32 divisors. Its prime factorisation is × 3 × 7 × 13. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 39, 42 … 2184.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
2184 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
2184 is composite. Its prime factorisation is
- 3
The divisors add up to 6720; without 2184 itself that is 4536, so 2184 is abundant (4536 is more than 2184). Euler's totient φ(2184) = 576 numbers up to 2184 share no factor with it.
- 4
The digits of 2184 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2184 = 2^{3} \times 3 \times 7 \times 13 \]2184 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 6720 |
| Euler totient φ(n) | 576 |
| Square | 4769856 |
| Cube | 10417365504 |
| Square root | 46.733286 (= 2√546) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 32 |
| Scientific notation | 2.184 × |
2184 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and eighty-four |
| Roman numerals | MMCLXXXIV |
| Binary (base 2) | 100010001000 |
| Octal (base 8) | 4210 |
| Hexadecimal (base 16) | 888 |
| Base 3 | 2222220 |
| As time | 2184 seconds = 36 min 24 s |
Is 2184 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2184 ÷ 2 = 1092) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2184 ÷ 3 = 728) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2184 ÷ 4 = 546) | 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 (2184 ÷ 6 = 364) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (2184 ÷ 7 = 312) | 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 (2184 ÷ 8 = 273) | 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 (2184 ÷ 12 = 182) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2184 a prime number?
No. 2184 = × 3 × 7 × 13, so it is divisible by 2.
What are the factors of 2184?
1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 273, 312, 364, 546, 728, 1092, 2184.
What is 2184 in binary?
100010001000 (hexadecimal 888, octal 4210).
What is the square root of 2184?
About 46.7333, exactly 2√546.
What is 2184 in Roman numerals?
MMCLXXXIV.
Is 2184 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 2184?
It is a composite number with 32 divisors.