The number 6000
6000 is a composite number with 40 divisors. Its prime factorisation is × 3 × . Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40 … 6000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6000: a Harshad number: divisible by its digit sum 6.
- 2
6000 is composite. Its prime factorisation is
- 3
The divisors add up to 19344; without 6000 itself that is 13344, so 6000 is abundant (13344 is more than 6000). Euler's totient φ(6000) = 1600 numbers up to 6000 share no factor with it.
- 4
The digits of 6000 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 6000 = 2^{4} \times 3 \times 5^{3} \]6000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 19344 |
| Euler totient φ(n) | 1600 |
| Square | 36000000 |
| Cube | 216000000000 |
| Square root | 77.459667 (= 20√15) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 49 |
| Scientific notation | 6 × |
6000 in other forms
| Form | Value |
|---|---|
| In words | six thousand |
| Binary (base 2) | 1011101110000 |
| Octal (base 8) | 13560 |
| Hexadecimal (base 16) | 1770 |
| Base 3 | 22020020 |
| As time | 6000 seconds = 1 h 40 min 0 s |
Is 6000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (6000 ÷ 2 = 3000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (6000 ÷ 3 = 2000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (6000 ÷ 4 = 1500) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (6000 ÷ 5 = 1200) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (6000 ÷ 6 = 1000) | 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 | Yes (6000 ÷ 8 = 750) | 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 | Yes (6000 ÷ 10 = 600) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (6000 ÷ 12 = 500) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 6000 a prime number?
No. 6000 = × 3 × , so it is divisible by 2.
What are the factors of 6000?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, 6000.
What is 6000 in binary?
1011101110000 (hexadecimal 1770, octal 13560).
What is the square root of 6000?
About 77.4597, exactly 20√15.
Is 6000 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 6000?
6000 is a Harshad number: divisible by its digit sum 6.