The number 2006
2006 is a composite number with 8 divisors. Its prime factorisation is 2 × 17 × 59. Divisors (8): 1, 2, 17, 34, 59, 118, 1003, 2006.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
2006 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
2006 is composite. Its prime factorisation is
- 3
The divisors add up to 3240; without 2006 itself that is 1234, so 2006 is deficient (1234 is less than 2006). Euler's totient φ(2006) = 928 numbers up to 2006 share no factor with it.
- 4
The digits of 2006 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2006 = 2 \times 17 \times 59 \]
2006 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 3240 |
| Euler totient φ(n) | 928 |
| Square | 4024036 |
| Cube | 8072216216 |
| Square root | 44.788391 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 42 |
| Scientific notation | 2.006 × |
2006 in other forms
| Form | Value |
|---|---|
| In words | two thousand and six |
| Roman numerals | MMVI |
| Binary (base 2) | 11111010110 |
| Octal (base 8) | 3726 |
| Hexadecimal (base 16) | 7D6 |
| Base 3 | 2202022 |
| As time | 2006 seconds = 33 min 26 s |
Is 2006 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2006 ÷ 2 = 1003) | 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 | No (remainder 2) | 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 2) | 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 | No (remainder 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2006 a prime number?
No. 2006 = 2 × 17 × 59, so it is divisible by 2.
What are the factors of 2006?
1, 2, 17, 34, 59, 118, 1003, 2006.
What is 2006 in binary?
11111010110 (hexadecimal 7D6, octal 3726).
What is the square root of 2006?
About 44.7884.
What is 2006 in Roman numerals?
MMVI.
Is 2006 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 2006?
It is a composite number with 8 divisors.