The number 12006
12006 is a composite number with 24 divisors. Its prime factorisation is 2 × × 23 × 29. Divisors (24): 1, 2, 3, 6, 9, 18, 23, 29, 46, 58, 69, 87, 138, 174, 207, 261 … 12006.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12006: a Harshad number: divisible by its digit sum 9.
- 2
12006 is composite. Its prime factorisation is
- 3
The divisors add up to 28080; without 12006 itself that is 16074, so 12006 is abundant (16074 is more than 12006). Euler's totient φ(12006) = 3696 numbers up to 12006 share no factor with it.
- 4
The digits of 12006 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12006 = 2 \times 3^{2} \times 23 \times 29 \]12006 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 28080 |
| Euler totient φ(n) | 3696 |
| Square | 144144036 |
| Cube | 1730593296216 |
| Square root | 109.571894 (= 3√1334) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.2006 × |
12006 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand and six |
| Binary (base 2) | 10111011100110 |
| Octal (base 8) | 27346 |
| Hexadecimal (base 16) | 2EE6 |
| Base 3 | 121110200 |
| As time | 12006 seconds = 3 h 20 min 6 s |
Is 12006 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12006 ÷ 2 = 6003) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12006 ÷ 3 = 4002) | 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 (12006 ÷ 6 = 2001) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (12006 ÷ 9 = 1334) | 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 5) | 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 12006 a prime number?
No. 12006 = 2 × × 23 × 29, so it is divisible by 2.
What are the factors of 12006?
1, 2, 3, 6, 9, 18, 23, 29, 46, 58, 69, 87, 138, 174, 207, 261, 414, 522, 667, 1334, 2001, 4002, 6003, 12006.
What is 12006 in binary?
10111011100110 (hexadecimal 2EE6, octal 27346).
What is the square root of 12006?
About 109.5719, exactly 3√1334.
Is 12006 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 12006?
12006 is a Harshad number: divisible by its digit sum 9.