The number 324
324 is a perfect square (18²). Its prime factorisation is × . Divisors (15): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 324: a perfect square (18²); a Harshad number: divisible by its digit sum 9.
- 2
324 is composite. Its prime factorisation is
- 3
The divisors add up to 847; without 324 itself that is 523, so 324 is abundant (523 is more than 324). Euler's totient φ(324) = 108 numbers up to 324 share no factor with it.
- 4
The digits of 324 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 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 324 = 2^{2} \times 3^{4} \]324 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 847 |
| Euler totient φ(n) | 108 |
| Square | 104976 |
| Cube | 34012224 |
| Square root | 18 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 24 |
| Scientific notation | 3.24 × |
| Perfect power |
324 in other forms
| Form | Value |
|---|---|
| In words | three hundred and twenty-four |
| Roman numerals | CCCXXIV |
| Binary (base 2) | 101000100 |
| Octal (base 8) | 504 |
| Hexadecimal (base 16) | 144 |
| Base 3 | 110000 |
| As time | 324 seconds = 5 min 24 s |
Is 324 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (324 ÷ 2 = 162) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (324 ÷ 3 = 108) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (324 ÷ 4 = 81) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (324 ÷ 6 = 54) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (324 ÷ 9 = 36) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (324 ÷ 12 = 27) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 324 a prime number?
No. 324 = × , so it is divisible by 2.
What are the factors of 324?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.
What is 324 in binary?
101000100 (hexadecimal 144, octal 504).
What is the square root of 324?
18, because 18 × 18 = 324.
What is 324 in Roman numerals?
CCCXXIV.
Is 324 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 324?
324 is a perfect square (18²); a Harshad number: divisible by its digit sum 9.