The number 3006
3006 is a composite number with 12 divisors. Its prime factorisation is 2 × × 167. Divisors (12): 1, 2, 3, 6, 9, 18, 167, 334, 501, 1002, 1503, 3006.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3006: a Harshad number: divisible by its digit sum 9.
- 2
3006 is composite. Its prime factorisation is
- 3
The divisors add up to 6552; without 3006 itself that is 3546, so 3006 is abundant (3546 is more than 3006). Euler's totient φ(3006) = 996 numbers up to 3006 share no factor with it.
- 4
The digits of 3006 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 141 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3006 = 2 \times 3^{2} \times 167 \]3006 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 6552 |
| Euler totient φ(n) | 996 |
| Square | 9036036 |
| Cube | 27162324216 |
| Square root | 54.827001 (= 3√334) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 141 |
| Scientific notation | 3.006 × |
3006 in other forms
| Form | Value |
|---|---|
| In words | three thousand and six |
| Roman numerals | MMMVI |
| Binary (base 2) | 101110111110 |
| Octal (base 8) | 5676 |
| Hexadecimal (base 16) | BBE |
| Base 3 | 11010100 |
| As time | 3006 seconds = 50 min 6 s |
Is 3006 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3006 ÷ 2 = 1503) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3006 ÷ 3 = 1002) | 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 (3006 ÷ 6 = 501) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | Yes (3006 ÷ 9 = 334) | 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 3) | 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 3006 a prime number?
No. 3006 = 2 × × 167, so it is divisible by 2.
What are the factors of 3006?
1, 2, 3, 6, 9, 18, 167, 334, 501, 1002, 1503, 3006.
What is 3006 in binary?
101110111110 (hexadecimal BBE, octal 5676).
What is the square root of 3006?
About 54.8270, exactly 3√334.
What is 3006 in Roman numerals?
MMMVI.
Is 3006 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 3006?
3006 is a Harshad number: divisible by its digit sum 9.