The number 2012
2012 is a composite number with 6 divisors. Its prime factorisation is × 503. Divisors (6): 1, 2, 4, 503, 1006, 2012.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
2012 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
2012 is composite. Its prime factorisation is
- 3
The divisors add up to 3528; without 2012 itself that is 1516, so 2012 is deficient (1516 is less than 2012). Euler's totient φ(2012) = 1004 numbers up to 2012 share no factor with it.
- 4
The digits of 2012 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2012 = 2^{2} \times 503 \]2012 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 3528 |
| Euler totient φ(n) | 1004 |
| Square | 4048144 |
| Cube | 8144865728 |
| Square root | 44.855323 (= 2√503) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 68 |
| Scientific notation | 2.012 × |
2012 in other forms
| Form | Value |
|---|---|
| In words | two thousand and twelve |
| Roman numerals | MMXII |
| Binary (base 2) | 11111011100 |
| Octal (base 8) | 3734 |
| Hexadecimal (base 16) | 7DC |
| Base 3 | 2202112 |
| As time | 2012 seconds = 33 min 32 s |
Is 2012 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2012 ÷ 2 = 1006) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2012 ÷ 4 = 503) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 5) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2012 a prime number?
No. 2012 = × 503, so it is divisible by 2.
What are the factors of 2012?
1, 2, 4, 503, 1006, 2012.
What is 2012 in binary?
11111011100 (hexadecimal 7DC, octal 3734).
What is the square root of 2012?
About 44.8553, exactly 2√503.
What is 2012 in Roman numerals?
MMXII.
Is 2012 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 2012?
It is a composite number with 6 divisors.