The number 1323
1323 is a composite number with 12 divisors. Its prime factorisation is × . Divisors (12): 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1323: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
1323 is composite. Its prime factorisation is
- 3
The divisors add up to 2280; without 1323 itself that is 957, so 1323 is deficient (957 is less than 1323). Euler's totient φ(1323) = 756 numbers up to 1323 share no factor with it.
- 4
The digits of 1323 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 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1323 = 3^{3} \times 7^{2} \]1323 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 2280 |
| Euler totient φ(n) | 756 |
| Square | 1750329 |
| Cube | 2315685267 |
| Square root | 36.373067 (= 21√3) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 1.323 × |
1323 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and twenty-three |
| Roman numerals | MCCCXXIII |
| Binary (base 2) | 10100101011 |
| Octal (base 8) | 2453 |
| Hexadecimal (base 16) | 52B |
| Base 3 | 1211000 |
| As time | 1323 seconds = 22 min 3 s |
Is 1323 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 (1323 ÷ 3 = 441) | 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 | Yes (1323 ÷ 7 = 189) | 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 (1323 ÷ 9 = 147) | 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 3) | 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 1323 a prime number?
No. 1323 = × , so it is divisible by 3.
What are the factors of 1323?
1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323.
What is 1323 in binary?
10100101011 (hexadecimal 52B, octal 2453).
What is the square root of 1323?
About 36.3731, exactly 21√3.
What is 1323 in Roman numerals?
MCCCXXIII.
Is 1323 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1323?
1323 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.