The number 2001
2001 is a composite number with 8 divisors. Its prime factorisation is 3 × 23 × 29. Divisors (8): 1, 3, 23, 29, 69, 87, 667, 2001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2001: a Harshad number: divisible by its digit sum 3.
- 2
2001 is composite. Its prime factorisation is
- 3
The divisors add up to 2880; without 2001 itself that is 879, so 2001 is deficient (879 is less than 2001). Euler's totient φ(2001) = 1232 numbers up to 2001 share no factor with it.
- 4
The digits of 2001 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 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2001 = 3 \times 23 \times 29 \]
2001 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2880 |
| Euler totient φ(n) | 1232 |
| Square | 4004001 |
| Cube | 8012006001 |
| Square root | 44.732538 |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 50 |
| Scientific notation | 2.001 × |
2001 in other forms
| Form | Value |
|---|---|
| In words | two thousand and one |
| Roman numerals | MMI |
| Binary (base 2) | 11111010001 |
| Octal (base 8) | 3721 |
| Hexadecimal (base 16) | 7D1 |
| Base 3 | 2202010 |
| As time | 2001 seconds = 33 min 21 s |
Is 2001 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2001 ÷ 3 = 667) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 1) | 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 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2001 a prime number?
No. 2001 = 3 × 23 × 29, so it is divisible by 3.
What are the factors of 2001?
1, 3, 23, 29, 69, 87, 667, 2001.
What is 2001 in binary?
11111010001 (hexadecimal 7D1, octal 3721).
What is the square root of 2001?
About 44.7325.
What is 2001 in Roman numerals?
MMI.
Is 2001 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 2001?
2001 is a Harshad number: divisible by its digit sum 3.