The number 12000
12000 is a composite number with 48 divisors. Its prime factorisation is × 3 × . Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32 … 12000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12000: a Harshad number: divisible by its digit sum 3.
- 2
12000 is composite. Its prime factorisation is
- 3
The divisors add up to 39312; without 12000 itself that is 27312, so 12000 is abundant (27312 is more than 12000). Euler's totient φ(12000) = 3200 numbers up to 12000 share no factor with it.
- 4
The digits of 12000 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
\[ 12000 = 2^{5} \times 3 \times 5^{3} \]12000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 39312 |
| Euler totient φ(n) | 3200 |
| Square | 144000000 |
| Cube | 1728000000000 |
| Square root | 109.544512 (= 20√30) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.2 × |
12000 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand |
| Binary (base 2) | 10111011100000 |
| Octal (base 8) | 27340 |
| Hexadecimal (base 16) | 2EE0 |
| Base 3 | 121110110 |
| As time | 12000 seconds = 3 h 20 min 0 s |
Is 12000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12000 ÷ 2 = 6000) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12000 ÷ 3 = 4000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12000 ÷ 4 = 3000) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (12000 ÷ 5 = 2400) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12000 ÷ 6 = 2000) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (12000 ÷ 8 = 1500) | 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 | Yes (12000 ÷ 10 = 1200) | 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 | Yes (12000 ÷ 12 = 1000) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12000 a prime number?
No. 12000 = × 3 × , so it is divisible by 2.
What are the factors of 12000?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 125, 150, 160, 200, 240, 250, 300, 375, 400, 480, 500, 600, 750, 800, 1000, 1200, 1500, 2000, 2400, 3000, 4000, 6000, 12000.
What is 12000 in binary?
10111011100000 (hexadecimal 2EE0, octal 27340).
What is the square root of 12000?
About 109.5445, exactly 20√30.
Is 12000 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 12000?
12000 is a Harshad number: divisible by its digit sum 3.