The number 2112
2112 is a palindrome: it reads 2112 backwards too. Its prime factorisation is × 3 × 11. Divisors (28): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64 … 2112.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2112: a palindrome: it reads 2112 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.
- 2
2112 is composite. Its prime factorisation is
- 3
The divisors add up to 6096; without 2112 itself that is 3984, so 2112 is abundant (3984 is more than 2112). Euler's totient φ(2112) = 640 numbers up to 2112 share no factor with it.
- 4
The digits of 2112 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2112 = 2^{6} \times 3 \times 11 \]2112 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 6096 |
| Euler totient φ(n) | 640 |
| Square | 4460544 |
| Cube | 9420668928 |
| Square root | 45.956501 (= 8√33) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 32 |
| Scientific notation | 2.112 × |
2112 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred and twelve |
| Roman numerals | MMCXII |
| Binary (base 2) | 100001000000 |
| Octal (base 8) | 4100 |
| Hexadecimal (base 16) | 840 |
| Base 3 | 2220020 |
| As time | 2112 seconds = 35 min 12 s |
Is 2112 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2112 ÷ 2 = 1056) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2112 ÷ 3 = 704) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2112 ÷ 4 = 528) | 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 (2112 ÷ 6 = 352) | 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 (2112 ÷ 8 = 264) | 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 (2112 ÷ 11 = 192) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2112 ÷ 12 = 176) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2112 a prime number?
No. 2112 = × 3 × 11, so it is divisible by 2.
What are the factors of 2112?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 132, 176, 192, 264, 352, 528, 704, 1056, 2112.
What is 2112 in binary?
100001000000 (hexadecimal 840, octal 4100).
What is the square root of 2112?
About 45.9565, exactly 8√33.
What is 2112 in Roman numerals?
MMCXII.
Is 2112 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 2112?
2112 is a palindrome: it reads 2112 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.