The number 12321
12321 is a perfect square (111²) and a palindrome: it reads 12321 backwards too. Its prime factorisation is × . Divisors (9): 1, 3, 9, 37, 111, 333, 1369, 4107, 12321.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12321: a perfect square (111²); a palindrome: it reads 12321 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
12321 is composite. Its prime factorisation is
- 3
The divisors add up to 18291; without 12321 itself that is 5970, so 12321 is deficient (5970 is less than 12321). Euler's totient φ(12321) = 7992 numbers up to 12321 share no factor with it.
- 4
The digits of 12321 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 156 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12321 = 3^{2} \times 37^{2} \]12321 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 9 |
| Sum of divisors | 18291 |
| Euler totient φ(n) | 7992 |
| Square | 151807041 |
| Cube | 1870414552161 |
| Square root | 111 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 156 |
| Scientific notation | 1.2321 × |
| Perfect power |
12321 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand three hundred and twenty-one |
| Binary (base 2) | 11000000100001 |
| Octal (base 8) | 30041 |
| Hexadecimal (base 16) | 3021 |
| Base 3 | 121220100 |
| As time | 12321 seconds = 3 h 25 min 21 s |
Is 12321 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 (12321 ÷ 3 = 4107) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 1) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (12321 ÷ 9 = 1369) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12321 a prime number?
No. 12321 = × , so it is divisible by 3.
What are the factors of 12321?
1, 3, 9, 37, 111, 333, 1369, 4107, 12321.
What is 12321 in binary?
11000000100001 (hexadecimal 3021, octal 30041).
What is the square root of 12321?
111, because 111 × 111 = 12321.
Is 12321 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 12321?
12321 is a perfect square (111²); a palindrome: it reads 12321 backwards too; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.