Number dictionary · Exact arithmetic
324: factors and number facts
three hundred twenty-four is an even number and is composite. Its 15 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred twenty-four
- Roman numeral
- CCCXXIV
- Prime factorization
- 2^2 × 3^4
- Digital root
- 9
All factors of 324
A positive factor divides 324 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
Factor pairs
- 1 × 324 = 324
- 2 × 162 = 324
- 3 × 108 = 324
- 4 × 81 = 324
- 6 × 54 = 324
- 9 × 36 = 324
- 12 × 27 = 324
- 18 × 18 = 324
Each pair describes an arrangement of 324 items into equal rows. The 18 × 18 pair is square, so its shared factor appears only once in the factor list.
Divisor totals
- Positive divisors
- 15
- Sum of all divisors
- 847
- Sum excluding 324
- 523
- Classification
- abundant
324 is abundant because its proper divisors add to 523, which is greater than 324.
Prime factorization of 324
324 = 2^2 × 3^4
Repeated division, step by step
- 324 ÷ 2 = 162
- 162 ÷ 2 = 81
- 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
Multiply the prime divisors in these steps to reconstruct 324. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (4 + 1) = 15.
The preceding prime is 317. The next larger prime is 331. The factor list above explains why 324 is composite.
Learn the factorization method324 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred twenty-four |
| Roman numeral | CCCXXIV |
| Binary (base 2) | 101000100 |
| Octal (base 8) | 504 |
| Decimal (base 10) | 324 |
| Hexadecimal (base 16) | 144 |
Check the binary conversion
Read 101000100 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 64 + 4 = 324
Check the hexadecimal conversion
1 × 16^2 + 4 × 16^1 + 4 × 16^0 = 324
Hexadecimal uses A through F for digit values 10 through 15. These notations represent the same quantity; changing the base does not change the integer.
Square, cube and square root of 324
- 324 squared
- 324 × 324 = 104,976
- 324 cubed
- 324 × 324 × 324 = 34,012,224
- Square root
- = 18
- Simplified radical
- 18
324 is a perfect square: 18 × 18 = 324. It is not a perfect cube.
324 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 324.
Distinguish a square from a square rootMultiplication table for 324
These are the first twelve positive multiples. Unlike the finite factor list, the sequence of multiples continues without an upper limit.
Divisibility checks
| Divide by | Whole quotient | Remainder | Divides exactly? |
|---|---|---|---|
| 2 | 162 | 0 | Yes |
| 3 | 108 | 0 | Yes |
| 4 | 81 | 0 | Yes |
| 5 | 64 | 4 | No |
| 6 | 54 | 0 | Yes |
| 7 | 46 | 2 | No |
| 8 | 40 | 4 | No |
| 9 | 36 | 0 | Yes |
| 10 | 32 | 4 | No |
| 11 | 29 | 5 | No |
| 12 | 27 | 0 | Yes |
For example, 324 = 7 × 46 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 324
324 contains 3 decimal digits. Its digit sum is 3 + 2 + 4 = 9.
- 324: 3 + 2 + 4 = 9
The digital root is 9. Reversing its digits gives 423; it is not a decimal palindrome. Digit patterns depend on the notation being used.
Digital-root arithmetic always finishes at a single digit for a positive integer. Some numerology methods stop at 11, 22 or 33 instead; that is a separate interpretive convention.
Fractions and a worked comparison
As a fraction of 100, 324/100 simplifies to 81/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 3.24. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 324 and 12 is 12. Their least common multiple is 324. The identity GCD × LCM = 324 × 12 = 3888 checks both results.
Work through GCF and LCMQuestions about 324
What are the factors of 324?
The positive factors are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324. There are 15 factors, including 1 and 324.
Is 324 a prime number?
No. 324 is composite: 2^2 × 3^4 = 324.
How do you write 324 in Roman numerals?
324 is CCCXXIV in standard subtractive Roman numeral notation.
What is the binary representation of 324?
324 in decimal is 101000100 in base 2. Adding its active place values gives 256 + 64 + 4 = 324.
Methods and reference definitions
Number JD calculates each result from the integer on this page. Positive factors are enumerated in pairs; repeated division gives the prime factorization; place values verify base conversions. Decimal square roots are rounded to six places when irrational.
NUMBER JOURNAL / JD
A reflective note on 324
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 324 add to 9. That arithmetic result is separate from the cultural symbolism of the pattern. If this number matters to you, write down what you noticed and choose one grounded action rather than treating the sighting as a prediction.