The number 12072
12072 is a composite number with 16 divisors. Its prime factorisation is × 3 × 503. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 503, 1006, 1509, 2012, 3018, 4024, 6036, 12072.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12072: a Harshad number: divisible by its digit sum 12.
- 2
12072 is composite. Its prime factorisation is
- 3
The divisors add up to 30240; without 12072 itself that is 18168, so 12072 is abundant (18168 is more than 12072). Euler's totient φ(12072) = 4016 numbers up to 12072 share no factor with it.
- 4
The digits of 12072 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 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12072 = 2^{3} \times 3 \times 503 \]12072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 30240 |
| Euler totient φ(n) | 4016 |
| Square | 145733184 |
| Cube | 1759290997248 |
| Square root | 109.872654 (= 2√3018) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 68 |
| Scientific notation | 1.2072 × |
12072 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand and seventy-two |
| Binary (base 2) | 10111100101000 |
| Octal (base 8) | 27450 |
| Hexadecimal (base 16) | 2F28 |
| Base 3 | 121120010 |
| As time | 12072 seconds = 3 h 21 min 12 s |
Is 12072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12072 ÷ 2 = 6036) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12072 ÷ 3 = 4024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12072 ÷ 4 = 3018) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12072 ÷ 6 = 2012) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (12072 ÷ 8 = 1509) | 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 2) | 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 | Yes (12072 ÷ 12 = 1006) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12072 a prime number?
No. 12072 = × 3 × 503, so it is divisible by 2.
What are the factors of 12072?
1, 2, 3, 4, 6, 8, 12, 24, 503, 1006, 1509, 2012, 3018, 4024, 6036, 12072.
What is 12072 in binary?
10111100101000 (hexadecimal 2F28, octal 27450).
What is the square root of 12072?
About 109.8727, exactly 2√3018.
Is 12072 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 12072?
12072 is a Harshad number: divisible by its digit sum 12.