Number dictionary · Exact arithmetic
429: factors and number facts
four hundred twenty-nine is an odd number and is composite. Its 8 positive divisors form 4 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- four hundred twenty-nine
- Roman numeral
- CDXXIX
- Prime factorization
- 3 × 11 × 13
- Digital root
- 6
All factors of 429
A positive factor divides 429 with no remainder. In ascending order, the complete list is:
1, 3, 11, 13, 33, 39, 143, 429
Factor pairs
- 1 × 429 = 429
- 3 × 143 = 429
- 11 × 39 = 429
- 13 × 33 = 429
Each pair describes an arrangement of 429 items into equal rows. The pairs have different row and column counts; 429 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 672
- Sum excluding 429
- 243
- Classification
- deficient
429 is deficient because its proper divisors add to 243, which is less than 429.
Prime factorization of 429
429 = 3 × 11 × 13
Repeated division, step by step
- 429 ÷ 3 = 143
- 143 ÷ 11 = 13
- 13 ÷ 13 = 1
Multiply the prime divisors in these steps to reconstruct 429. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) × (1 + 1) = 8.
The preceding prime is 421. The next larger prime is 431. The factor list above explains why 429 is composite.
Learn the factorization method429 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred twenty-nine |
| Roman numeral | CDXXIX |
| Binary (base 2) | 110101101 |
| Octal (base 8) | 655 |
| Decimal (base 10) | 429 |
| Hexadecimal (base 16) | 1AD |
Check the binary conversion
Read 110101101 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 128 + 32 + 8 + 4 + 1 = 429
Check the hexadecimal conversion
1 × 16^2 + 10 × 16^1 + 13 × 16^0 = 429
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 429
- 429 squared
- 429 × 429 = 184,041
- 429 cubed
- 429 × 429 × 429 = 78,953,589
- Square root
- ≈ 20.712315
- Simplified radical
- √429
429 lies between 400 (20²) and 441 (21²), so it is not a perfect square. It is not a perfect cube.
429 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 429.
Distinguish a square from a square rootMultiplication table for 429
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 | 214 | 1 | No |
| 3 | 143 | 0 | Yes |
| 4 | 107 | 1 | No |
| 5 | 85 | 4 | No |
| 6 | 71 | 3 | No |
| 7 | 61 | 2 | No |
| 8 | 53 | 5 | No |
| 9 | 47 | 6 | No |
| 10 | 42 | 9 | No |
| 11 | 39 | 0 | Yes |
| 12 | 35 | 9 | No |
For example, 429 = 7 × 61 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 429
429 contains 3 decimal digits. Its digit sum is 4 + 2 + 9 = 15.
- 429: 4 + 2 + 9 = 15
- 15: 1 + 5 = 6
The digital root is 6. Reversing its digits gives 924; 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, 429/100 simplifies to 429/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 4.29. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 429 and 12 is 3. Their least common multiple is 1716. The identity GCD × LCM = 429 × 12 = 5148 checks both results.
Work through GCF and LCMQuestions about 429
What are the factors of 429?
The positive factors are 1, 3, 11, 13, 33, 39, 143, 429. There are 8 factors, including 1 and 429.
Is 429 a prime number?
No. 429 is composite: 3 × 11 × 13 = 429.
How do you write 429 in Roman numerals?
429 is CDXXIX in standard subtractive Roman numeral notation.
What is the binary representation of 429?
429 in decimal is 110101101 in base 2. Adding its active place values gives 256 + 128 + 32 + 8 + 4 + 1 = 429.
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 429
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 429 add to 15. 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.