Number dictionary · Exact arithmetic
426: factors and number facts
four hundred twenty-six is an even 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-six
- Roman numeral
- CDXXVI
- Prime factorization
- 2 × 3 × 71
- Digital root
- 3
All factors of 426
A positive factor divides 426 with no remainder. In ascending order, the complete list is:
1, 2, 3, 6, 71, 142, 213, 426
Factor pairs
- 1 × 426 = 426
- 2 × 213 = 426
- 3 × 142 = 426
- 6 × 71 = 426
Each pair describes an arrangement of 426 items into equal rows. The pairs have different row and column counts; 426 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 864
- Sum excluding 426
- 438
- Classification
- abundant
426 is abundant because its proper divisors add to 438, which is greater than 426.
Prime factorization of 426
426 = 2 × 3 × 71
Repeated division, step by step
- 426 ÷ 2 = 213
- 213 ÷ 3 = 71
- 71 ÷ 71 = 1
Multiply the prime divisors in these steps to reconstruct 426. 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 426 is composite.
Learn the factorization method426 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred twenty-six |
| Roman numeral | CDXXVI |
| Binary (base 2) | 110101010 |
| Octal (base 8) | 652 |
| Decimal (base 10) | 426 |
| Hexadecimal (base 16) | 1AA |
Check the binary conversion
Read 110101010 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 + 2 = 426
Check the hexadecimal conversion
1 × 16^2 + 10 × 16^1 + 10 × 16^0 = 426
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 426
- 426 squared
- 426 × 426 = 181,476
- 426 cubed
- 426 × 426 × 426 = 77,308,776
- Square root
- ≈ 20.639767
- Simplified radical
- √426
426 lies between 400 (20²) and 441 (21²), so it is not a perfect square. It is not a perfect cube.
426 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 426.
Distinguish a square from a square rootMultiplication table for 426
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 | 213 | 0 | Yes |
| 3 | 142 | 0 | Yes |
| 4 | 106 | 2 | No |
| 5 | 85 | 1 | No |
| 6 | 71 | 0 | Yes |
| 7 | 60 | 6 | No |
| 8 | 53 | 2 | No |
| 9 | 47 | 3 | No |
| 10 | 42 | 6 | No |
| 11 | 38 | 8 | No |
| 12 | 35 | 6 | No |
For example, 426 = 7 × 60 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 426
426 contains 3 decimal digits. Its digit sum is 4 + 2 + 6 = 12.
- 426: 4 + 2 + 6 = 12
- 12: 1 + 2 = 3
The digital root is 3. Reversing its digits gives 624; 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, 426/100 simplifies to 213/50 by dividing both terms by their greatest common divisor, 2. Its decimal value is 4.26. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 426 and 12 is 6. Their least common multiple is 852. The identity GCD × LCM = 426 × 12 = 5112 checks both results.
Work through GCF and LCMQuestions about 426
What are the factors of 426?
The positive factors are 1, 2, 3, 6, 71, 142, 213, 426. There are 8 factors, including 1 and 426.
Is 426 a prime number?
No. 426 is composite: 2 × 3 × 71 = 426.
How do you write 426 in Roman numerals?
426 is CDXXVI in standard subtractive Roman numeral notation.
What is the binary representation of 426?
426 in decimal is 110101010 in base 2. Adding its active place values gives 256 + 128 + 32 + 8 + 2 = 426.
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 426
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 426 add to 12. 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.