The number 6084
6084 is a perfect square (78²). Its prime factorisation is × × . Divisors (27): 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156 … 6084.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6084: a perfect square (78²); a Harshad number: divisible by its digit sum 18.
- 2
6084 is composite. Its prime factorisation is
- 3
The divisors add up to 16653; without 6084 itself that is 10569, so 6084 is abundant (10569 is more than 6084). Euler's totient φ(6084) = 1872 numbers up to 6084 share no factor with it.
- 4
The digits of 6084 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 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 6084 = 2^{2} \times 3^{2} \times 13^{2} \]6084 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 16653 |
| Euler totient φ(n) | 1872 |
| Square | 37015056 |
| Cube | 225199600704 |
| Square root | 78 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 111 |
| Scientific notation | 6.084 × |
| Perfect power |
6084 in other forms
| Form | Value |
|---|---|
| In words | six thousand and eighty-four |
| Binary (base 2) | 1011111000100 |
| Octal (base 8) | 13704 |
| Hexadecimal (base 16) | 17C4 |
| Base 3 | 22100100 |
| As time | 6084 seconds = 1 h 41 min 24 s |
Is 6084 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (6084 ÷ 2 = 3042) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (6084 ÷ 3 = 2028) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (6084 ÷ 4 = 1521) | 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 (6084 ÷ 6 = 1014) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (6084 ÷ 9 = 676) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (6084 ÷ 12 = 507) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 6084 a prime number?
No. 6084 = × × , so it is divisible by 2.
What are the factors of 6084?
1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 169, 234, 338, 468, 507, 676, 1014, 1521, 2028, 3042, 6084.
What is 6084 in binary?
1011111000100 (hexadecimal 17C4, octal 13704).
What is the square root of 6084?
78, because 78 × 78 = 6084.
Is 6084 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 6084?
6084 is a perfect square (78²); a Harshad number: divisible by its digit sum 18.