Number dictionary · Exact arithmetic
329: factors and number facts
three hundred twenty-nine is an odd number and is composite. Its 4 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred twenty-nine
- Roman numeral
- CCCXXIX
- Prime factorization
- 7 × 47
- Digital root
- 5
All factors of 329
A positive factor divides 329 with no remainder. In ascending order, the complete list is:
1, 7, 47, 329
Factor pairs
- 1 × 329 = 329
- 7 × 47 = 329
Each pair describes an arrangement of 329 items into equal rows. The pairs have different row and column counts; 329 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 384
- Sum excluding 329
- 55
- Classification
- deficient
329 is deficient because its proper divisors add to 55, which is less than 329.
Prime factorization of 329
329 = 7 × 47
Repeated division, step by step
- 329 ÷ 7 = 47
- 47 ÷ 47 = 1
Multiply the prime divisors in these steps to reconstruct 329. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 317. The next larger prime is 331. The factor list above explains why 329 is composite.
Learn the factorization method329 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred twenty-nine |
| Roman numeral | CCCXXIX |
| Binary (base 2) | 101001001 |
| Octal (base 8) | 511 |
| Decimal (base 10) | 329 |
| Hexadecimal (base 16) | 149 |
Check the binary conversion
Read 101001001 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 + 8 + 1 = 329
Check the hexadecimal conversion
1 × 16^2 + 4 × 16^1 + 9 × 16^0 = 329
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 329
- 329 squared
- 329 × 329 = 108,241
- 329 cubed
- 329 × 329 × 329 = 35,611,289
- Square root
- ≈ 18.138357
- Simplified radical
- √329
329 lies between 324 (18²) and 361 (19²), so it is not a perfect square. It is not a perfect cube.
329 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 329.
Distinguish a square from a square rootMultiplication table for 329
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 | 164 | 1 | No |
| 3 | 109 | 2 | No |
| 4 | 82 | 1 | No |
| 5 | 65 | 4 | No |
| 6 | 54 | 5 | No |
| 7 | 47 | 0 | Yes |
| 8 | 41 | 1 | No |
| 9 | 36 | 5 | No |
| 10 | 32 | 9 | No |
| 11 | 29 | 10 | No |
| 12 | 27 | 5 | No |
For example, 329 = 7 × 47 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 329
329 contains 3 decimal digits. Its digit sum is 3 + 2 + 9 = 14.
- 329: 3 + 2 + 9 = 14
- 14: 1 + 4 = 5
The digital root is 5. Reversing its digits gives 923; 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, 329/100 simplifies to 329/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 3.29. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 329 and 12 is 1. Their least common multiple is 3948. The identity GCD × LCM = 329 × 12 = 3948 checks both results.
Work through GCF and LCMQuestions about 329
What are the factors of 329?
The positive factors are 1, 7, 47, 329. There are 4 factors, including 1 and 329.
Is 329 a prime number?
No. 329 is composite: 7 × 47 = 329.
How do you write 329 in Roman numerals?
329 is CCCXXIX in standard subtractive Roman numeral notation.
What is the binary representation of 329?
329 in decimal is 101001001 in base 2. Adding its active place values gives 256 + 64 + 8 + 1 = 329.
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 329
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 329 add to 14. 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.