Number dictionary · Exact arithmetic
508: factors and number facts
five hundred eight is an even number and is composite. Its 6 positive divisors form 3 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- five hundred eight
- Roman numeral
- DVIII
- Prime factorization
- 2^2 × 127
- Digital root
- 4
All factors of 508
A positive factor divides 508 with no remainder. In ascending order, the complete list is:
1, 2, 4, 127, 254, 508
Factor pairs
- 1 × 508 = 508
- 2 × 254 = 508
- 4 × 127 = 508
Each pair describes an arrangement of 508 items into equal rows. The pairs have different row and column counts; 508 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 6
- Sum of all divisors
- 896
- Sum excluding 508
- 388
- Classification
- deficient
508 is deficient because its proper divisors add to 388, which is less than 508.
Prime factorization of 508
508 = 2^2 × 127
Repeated division, step by step
- 508 ÷ 2 = 254
- 254 ÷ 2 = 127
- 127 ÷ 127 = 1
Multiply the prime divisors in these steps to reconstruct 508. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (1 + 1) = 6.
The preceding prime is 503. The next larger prime is 509. The factor list above explains why 508 is composite.
Learn the factorization method508 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | five hundred eight |
| Roman numeral | DVIII |
| Binary (base 2) | 111111100 |
| Octal (base 8) | 774 |
| Decimal (base 10) | 508 |
| Hexadecimal (base 16) | 1FC |
Check the binary conversion
Read 111111100 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 + 64 + 32 + 16 + 8 + 4 = 508
Check the hexadecimal conversion
1 × 16^2 + 15 × 16^1 + 12 × 16^0 = 508
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 508
- 508 squared
- 508 × 508 = 258,064
- 508 cubed
- 508 × 508 × 508 = 131,096,512
- Square root
- ≈ 22.538855
- Simplified radical
- 2√127
508 lies between 484 (22²) and 529 (23²), so it is not a perfect square. It is not a perfect cube.
508 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 508.
Distinguish a square from a square rootMultiplication table for 508
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 | 254 | 0 | Yes |
| 3 | 169 | 1 | No |
| 4 | 127 | 0 | Yes |
| 5 | 101 | 3 | No |
| 6 | 84 | 4 | No |
| 7 | 72 | 4 | No |
| 8 | 63 | 4 | No |
| 9 | 56 | 4 | No |
| 10 | 50 | 8 | No |
| 11 | 46 | 2 | No |
| 12 | 42 | 4 | No |
For example, 508 = 7 × 72 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 508
508 contains 3 decimal digits. Its digit sum is 5 + 0 + 8 = 13.
- 508: 5 + 0 + 8 = 13
- 13: 1 + 3 = 4
The digital root is 4. Reversing its digits gives 805; 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, 508/100 simplifies to 127/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 5.08. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 508 and 12 is 4. Their least common multiple is 1524. The identity GCD × LCM = 508 × 12 = 6096 checks both results.
Work through GCF and LCMQuestions about 508
What are the factors of 508?
The positive factors are 1, 2, 4, 127, 254, 508. There are 6 factors, including 1 and 508.
Is 508 a prime number?
No. 508 is composite: 2^2 × 127 = 508.
How do you write 508 in Roman numerals?
508 is DVIII in standard subtractive Roman numeral notation.
What is the binary representation of 508?
508 in decimal is 111111100 in base 2. Adding its active place values gives 256 + 128 + 64 + 32 + 16 + 8 + 4 = 508.
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 508
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 508 add to 13. 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.