The number 2000
2000 is a composite number with 20 divisors. Its prime factorisation is × . Divisors (20): 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250 … 2000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2000: a Harshad number: divisible by its digit sum 2.
- 2
2000 is composite. Its prime factorisation is
- 3
The divisors add up to 4836; without 2000 itself that is 2836, so 2000 is abundant (2836 is more than 2000). Euler's totient φ(2000) = 800 numbers up to 2000 share no factor with it.
- 4
The digits of 2000 add up to 2, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2000 = 2^{4} \times 5^{3} \]2000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 4836 |
| Euler totient φ(n) | 800 |
| Square | 4000000 |
| Cube | 8000000000 |
| Square root | 44.721360 (= 20√5) |
| Digit sum / digital root | 2 / 2 |
| Collatz steps to 1 | 112 |
| Scientific notation | 2 × |
2000 in other forms
| Form | Value |
|---|---|
| In words | two thousand |
| Roman numerals | MM |
| Binary (base 2) | 11111010000 |
| Octal (base 8) | 3720 |
| Hexadecimal (base 16) | 7D0 |
| Base 3 | 2202002 |
| As time | 2000 seconds = 33 min 20 s |
Is 2000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2000 ÷ 2 = 1000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2000 ÷ 4 = 500) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2000 ÷ 5 = 400) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (2000 ÷ 8 = 250) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2000 ÷ 10 = 200) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2000 a prime number?
No. 2000 = × , so it is divisible by 2.
What are the factors of 2000?
1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000.
What is 2000 in binary?
11111010000 (hexadecimal 7D0, octal 3720).
What is the square root of 2000?
About 44.7214, exactly 20√5.
What is 2000 in Roman numerals?
MM.
Is 2000 divisible by 3?
No. Its digits add up to 2, which is not a multiple of 3.
What is special about the number 2000?
2000 is a Harshad number: divisible by its digit sum 2.