The number 12024
12024 is a composite number with 24 divisors. Its prime factorisation is × × 167. Divisors (24): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 167, 334, 501, 668 … 12024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12024: a Harshad number: divisible by its digit sum 9.
- 2
12024 is composite. Its prime factorisation is
- 3
The divisors add up to 32760; without 12024 itself that is 20736, so 12024 is abundant (20736 is more than 12024). Euler's totient φ(12024) = 3984 numbers up to 12024 share no factor with it.
- 4
The digits of 12024 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 143 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12024 = 2^{3} \times 3^{2} \times 167 \]12024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 32760 |
| Euler totient φ(n) | 3984 |
| Square | 144576576 |
| Cube | 1738388749824 |
| Square root | 109.654001 (= 6√334) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 143 |
| Scientific notation | 1.2024 × |
12024 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand and twenty-four |
| Binary (base 2) | 10111011111000 |
| Octal (base 8) | 27370 |
| Hexadecimal (base 16) | 2EF8 |
| Base 3 | 121111100 |
| As time | 12024 seconds = 3 h 20 min 24 s |
Is 12024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12024 ÷ 2 = 6012) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12024 ÷ 3 = 4008) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12024 ÷ 4 = 3006) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12024 ÷ 6 = 2004) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (12024 ÷ 8 = 1503) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (12024 ÷ 9 = 1336) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12024 ÷ 12 = 1002) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12024 a prime number?
No. 12024 = × × 167, so it is divisible by 2.
What are the factors of 12024?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 167, 334, 501, 668, 1002, 1336, 1503, 2004, 3006, 4008, 6012, 12024.
What is 12024 in binary?
10111011111000 (hexadecimal 2EF8, octal 27370).
What is the square root of 12024?
About 109.6540, exactly 6√334.
Is 12024 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 12024?
12024 is a Harshad number: divisible by its digit sum 9.