Number dictionary · Exact arithmetic
424: factors and number facts
four hundred twenty-four 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-four
- Roman numeral
- CDXXIV
- Prime factorization
- 2^3 × 53
- Digital root
- 1
All factors of 424
A positive factor divides 424 with no remainder. In ascending order, the complete list is:
1, 2, 4, 8, 53, 106, 212, 424
Factor pairs
- 1 × 424 = 424
- 2 × 212 = 424
- 4 × 106 = 424
- 8 × 53 = 424
Each pair describes an arrangement of 424 items into equal rows. The pairs have different row and column counts; 424 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 810
- Sum excluding 424
- 386
- Classification
- deficient
424 is deficient because its proper divisors add to 386, which is less than 424.
Prime factorization of 424
424 = 2^3 × 53
Repeated division, step by step
- 424 ÷ 2 = 212
- 212 ÷ 2 = 106
- 106 ÷ 2 = 53
- 53 ÷ 53 = 1
Multiply the prime divisors in these steps to reconstruct 424. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) = 8.
The preceding prime is 421. The next larger prime is 431. The factor list above explains why 424 is composite.
Learn the factorization method424 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | four hundred twenty-four |
| Roman numeral | CDXXIV |
| Binary (base 2) | 110101000 |
| Octal (base 8) | 650 |
| Decimal (base 10) | 424 |
| Hexadecimal (base 16) | 1A8 |
Check the binary conversion
Read 110101000 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 = 424
Check the hexadecimal conversion
1 × 16^2 + 10 × 16^1 + 8 × 16^0 = 424
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 424
- 424 squared
- 424 × 424 = 179,776
- 424 cubed
- 424 × 424 × 424 = 76,225,024
- Square root
- ≈ 20.591260
- Simplified radical
- 2√106
424 lies between 400 (20²) and 441 (21²), so it is not a perfect square. It is not a perfect cube.
424 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 424.
Distinguish a square from a square rootMultiplication table for 424
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 | 212 | 0 | Yes |
| 3 | 141 | 1 | No |
| 4 | 106 | 0 | Yes |
| 5 | 84 | 4 | No |
| 6 | 70 | 4 | No |
| 7 | 60 | 4 | No |
| 8 | 53 | 0 | Yes |
| 9 | 47 | 1 | No |
| 10 | 42 | 4 | No |
| 11 | 38 | 6 | No |
| 12 | 35 | 4 | No |
For example, 424 = 7 × 60 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 424
424 contains 3 decimal digits. Its digit sum is 4 + 2 + 4 = 10.
- 424: 4 + 2 + 4 = 10
- 10: 1 + 0 = 1
The digital root is 1. 424 reads the same forward and backward, making it 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, 424/100 simplifies to 106/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 4.24. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 424 and 12 is 4. Their least common multiple is 1272. The identity GCD × LCM = 424 × 12 = 5088 checks both results.
Work through GCF and LCMQuestions about 424
What are the factors of 424?
The positive factors are 1, 2, 4, 8, 53, 106, 212, 424. There are 8 factors, including 1 and 424.
Is 424 a prime number?
No. 424 is composite: 2^3 × 53 = 424.
How do you write 424 in Roman numerals?
424 is CDXXIV in standard subtractive Roman numeral notation.
What is the binary representation of 424?
424 in decimal is 110101000 in base 2. Adding its active place values gives 256 + 128 + 32 + 8 = 424.
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 424
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 424 add to 10. 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.