The number 6006
6006 is a palindrome: it reads 6006 backwards too. Its prime factorisation is 2 × 3 × 7 × 11 × 13. Divisors (32): 1, 2, 3, 6, 7, 11, 13, 14, 21, 22, 26, 33, 39, 42, 66, 77 … 6006.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 6006: a palindrome: it reads 6006 backwards too.
- 2
6006 is composite. Its prime factorisation is
- 3
The divisors add up to 16128; without 6006 itself that is 10122, so 6006 is abundant (10122 is more than 6006). Euler's totient φ(6006) = 1440 numbers up to 6006 share no factor with it.
- 4
The digits of 6006 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 6006 = 2 \times 3 \times 7 \times 11 \times 13 \]
6006 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 16128 |
| Euler totient φ(n) | 1440 |
| Square | 36072036 |
| Cube | 216648648216 |
| Square root | 77.498387 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 41 |
| Scientific notation | 6.006 × |
6006 in other forms
| Form | Value |
|---|---|
| In words | six thousand and six |
| Binary (base 2) | 1011101110110 |
| Octal (base 8) | 13566 |
| Hexadecimal (base 16) | 1776 |
| Base 3 | 22020110 |
| As time | 6006 seconds = 1 h 40 min 6 s |
Is 6006 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (6006 ÷ 2 = 3003) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (6006 ÷ 3 = 2002) | 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 | Yes (6006 ÷ 6 = 1001) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (6006 ÷ 7 = 858) | 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 3) | 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 | Yes (6006 ÷ 11 = 546) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 6006 a prime number?
No. 6006 = 2 × 3 × 7 × 11 × 13, so it is divisible by 2.
What are the factors of 6006?
1, 2, 3, 6, 7, 11, 13, 14, 21, 22, 26, 33, 39, 42, 66, 77, 78, 91, 143, 154, 182, 231, 273, 286, 429, 462, 546, 858, 1001, 2002, 3003, 6006.
What is 6006 in binary?
1011101110110 (hexadecimal 1776, octal 13566).
What is the square root of 6006?
About 77.4984.
Is 6006 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 6006?
6006 is a palindrome: it reads 6006 backwards too.