The number 12123
12123 is a composite number with 8 divisors. Its prime factorisation is × 449. Divisors (8): 1, 3, 9, 27, 449, 1347, 4041, 12123.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12123: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
12123 is composite. Its prime factorisation is
- 3
The divisors add up to 18000; without 12123 itself that is 5877, so 12123 is deficient (5877 is less than 12123). Euler's totient φ(12123) = 8064 numbers up to 12123 share no factor with it.
- 4
The digits of 12123 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 81 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12123 = 3^{3} \times 449 \]12123 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 18000 |
| Euler totient φ(n) | 8064 |
| Square | 146967129 |
| Cube | 1781682504867 |
| Square root | 110.104496 (= 3√1347) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 81 |
| Scientific notation | 1.2123 × |
12123 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand one hundred and twenty-three |
| Binary (base 2) | 10111101011011 |
| Octal (base 8) | 27533 |
| Hexadecimal (base 16) | 2F5B |
| Base 3 | 121122000 |
| As time | 12123 seconds = 3 h 22 min 3 s |
Is 12123 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12123 ÷ 3 = 4041) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (12123 ÷ 9 = 1347) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12123 a prime number?
No. 12123 = × 449, so it is divisible by 3.
What are the factors of 12123?
1, 3, 9, 27, 449, 1347, 4041, 12123.
What is 12123 in binary?
10111101011011 (hexadecimal 2F5B, octal 27533).
What is the square root of 12123?
About 110.1045, exactly 3√1347.
Is 12123 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 12123?
12123 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.