The number 12012
12012 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 11 × 13. Divisors (48): 1, 2, 3, 4, 6, 7, 11, 12, 13, 14, 21, 22, 26, 28, 33, 39 … 12012.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12012: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.
- 2
12012 is composite. Its prime factorisation is
- 3
The divisors add up to 37632; without 12012 itself that is 25620, so 12012 is abundant (25620 is more than 12012). Euler's totient φ(12012) = 2880 numbers up to 12012 share no factor with it.
- 4
The digits of 12012 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12012 = 2^{2} \times 3 \times 7 \times 11 \times 13 \]12012 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 37632 |
| Euler totient φ(n) | 2880 |
| Square | 144288144 |
| Cube | 1733189185728 |
| Square root | 109.599270 (= 2√3003) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.2012 × |
12012 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand and twelve |
| Binary (base 2) | 10111011101100 |
| Octal (base 8) | 27354 |
| Hexadecimal (base 16) | 2EEC |
| Base 3 | 121110220 |
| As time | 12012 seconds = 3 h 20 min 12 s |
Is 12012 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12012 ÷ 2 = 6006) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12012 ÷ 3 = 4004) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12012 ÷ 4 = 3003) | 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 (12012 ÷ 6 = 2002) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (12012 ÷ 7 = 1716) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | Yes (12012 ÷ 11 = 1092) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (12012 ÷ 12 = 1001) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12012 a prime number?
No. 12012 = × 3 × 7 × 11 × 13, so it is divisible by 2.
What are the factors of 12012?
1, 2, 3, 4, 6, 7, 11, 12, 13, 14, 21, 22, 26, 28, 33, 39, 42, 44, 52, 66, 77, 78, 84, 91, 132, 143, 154, 156, 182, 231, 273, 286, 308, 364, 429, 462, 546, 572, 858, 924, 1001, 1092, 1716, 2002, 3003, 4004, 6006, 12012.
What is 12012 in binary?
10111011101100 (hexadecimal 2EEC, octal 27354).
What is the square root of 12012?
About 109.5993, exactly 2√3003.
Is 12012 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 12012?
12012 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.