The number 3000
3000 is a composite number with 32 divisors. Its prime factorisation is × 3 × . Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50 … 3000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3000: a Harshad number: divisible by its digit sum 3.
- 2
3000 is composite. Its prime factorisation is
- 3
The divisors add up to 9360; without 3000 itself that is 6360, so 3000 is abundant (6360 is more than 3000). Euler's totient φ(3000) = 800 numbers up to 3000 share no factor with it.
- 4
The digits of 3000 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3000 = 2^{3} \times 3 \times 5^{3} \]3000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 9360 |
| Euler totient φ(n) | 800 |
| Square | 9000000 |
| Cube | 27000000000 |
| Square root | 54.772256 (= 10√30) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 48 |
| Scientific notation | 3 × |
3000 in other forms
| Form | Value |
|---|---|
| In words | three thousand |
| Roman numerals | MMM |
| Binary (base 2) | 101110111000 |
| Octal (base 8) | 5670 |
| Hexadecimal (base 16) | BB8 |
| Base 3 | 11010010 |
| As time | 3000 seconds = 50 min 0 s |
Is 3000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3000 ÷ 2 = 1500) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3000 ÷ 3 = 1000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3000 ÷ 4 = 750) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (3000 ÷ 5 = 600) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (3000 ÷ 6 = 500) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (3000 ÷ 8 = 375) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (3000 ÷ 10 = 300) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3000 ÷ 12 = 250) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3000 a prime number?
No. 3000 = × 3 × , so it is divisible by 2.
What are the factors of 3000?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000.
What is 3000 in binary?
101110111000 (hexadecimal BB8, octal 5670).
What is the square root of 3000?
About 54.7723, exactly 10√30.
What is 3000 in Roman numerals?
MMM.
Is 3000 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 3000?
3000 is a Harshad number: divisible by its digit sum 3.