The number 12100
12100 is a perfect square (110²). Its prime factorisation is × × . Divisors (27): 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 121, 220 … 12100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12100: a perfect square (110²); a Harshad number: divisible by its digit sum 4.
- 2
12100 is composite. Its prime factorisation is
- 3
The divisors add up to 28861; without 12100 itself that is 16761, so 12100 is abundant (16761 is more than 12100). Euler's totient φ(12100) = 4400 numbers up to 12100 share no factor with it.
- 4
The digits of 12100 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12100 = 2^{2} \times 5^{2} \times 11^{2} \]12100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 28861 |
| Euler totient φ(n) | 4400 |
| Square | 146410000 |
| Cube | 1771561000000 |
| Square root | 110 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 68 |
| Scientific notation | 1.21 × |
| Perfect power |
12100 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand one hundred |
| Binary (base 2) | 10111101000100 |
| Octal (base 8) | 27504 |
| Hexadecimal (base 16) | 2F44 |
| Base 3 | 121121011 |
| As time | 12100 seconds = 3 h 21 min 40 s |
Is 12100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12100 ÷ 2 = 6050) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12100 ÷ 4 = 3025) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (12100 ÷ 5 = 2420) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (12100 ÷ 10 = 1210) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (12100 ÷ 11 = 1100) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12100 a prime number?
No. 12100 = × × , so it is divisible by 2.
What are the factors of 12100?
1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 121, 220, 242, 275, 484, 550, 605, 1100, 1210, 2420, 3025, 6050, 12100.
What is 12100 in binary?
10111101000100 (hexadecimal 2F44, octal 27504).
What is the square root of 12100?
110, because 110 × 110 = 12100.
Is 12100 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 12100?
12100 is a perfect square (110²); a Harshad number: divisible by its digit sum 4.