Number dictionary · Exact arithmetic
500: factors and number facts
five hundred is an even number and is composite. Its 12 positive divisors form 6 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- five hundred
- Roman numeral
- D
- Prime factorization
- 2^2 × 5^3
- Digital root
- 5
All factors of 500
A positive factor divides 500 with no remainder. In ascending order, the complete list is:
1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
Factor pairs
- 1 × 500 = 500
- 2 × 250 = 500
- 4 × 125 = 500
- 5 × 100 = 500
- 10 × 50 = 500
- 20 × 25 = 500
Each pair describes an arrangement of 500 items into equal rows. The pairs have different row and column counts; 500 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 12
- Sum of all divisors
- 1092
- Sum excluding 500
- 592
- Classification
- abundant
500 is abundant because its proper divisors add to 592, which is greater than 500.
Prime factorization of 500
500 = 2^2 × 5^3
Repeated division, step by step
- 500 ÷ 2 = 250
- 250 ÷ 2 = 125
- 125 ÷ 5 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
Multiply the prime divisors in these steps to reconstruct 500. An exponent records how many times the same prime occurs. The divisor-count calculation is (2 + 1) × (3 + 1) = 12.
The preceding prime is 499. The next larger prime is 503. The factor list above explains why 500 is composite.
Learn the factorization method500 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | five hundred |
| Roman numeral | D |
| Binary (base 2) | 111110100 |
| Octal (base 8) | 764 |
| Decimal (base 10) | 500 |
| Hexadecimal (base 16) | 1F4 |
Check the binary conversion
Read 111110100 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 + 4 = 500
Check the hexadecimal conversion
1 × 16^2 + 15 × 16^1 + 4 × 16^0 = 500
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 500
- 500 squared
- 500 × 500 = 250,000
- 500 cubed
- 500 × 500 × 500 = 125,000,000
- Square root
- ≈ 22.360680
- Simplified radical
- 10√5
500 lies between 484 (22²) and 529 (23²), so it is not a perfect square. It is not a perfect cube.
500 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 500.
Distinguish a square from a square rootMultiplication table for 500
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 | 250 | 0 | Yes |
| 3 | 166 | 2 | No |
| 4 | 125 | 0 | Yes |
| 5 | 100 | 0 | Yes |
| 6 | 83 | 2 | No |
| 7 | 71 | 3 | No |
| 8 | 62 | 4 | No |
| 9 | 55 | 5 | No |
| 10 | 50 | 0 | Yes |
| 11 | 45 | 5 | No |
| 12 | 41 | 8 | No |
For example, 500 = 7 × 71 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 500
500 contains 3 decimal digits. Its digit sum is 5 + 0 + 0 = 5.
- 500: 5 + 0 + 0 = 5
The digital root is 5. Reversing its digits gives 005; 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, 500/100 simplifies to 5/1 by dividing both terms by their greatest common divisor, 100. Its decimal value is 5. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 500 and 12 is 4. Their least common multiple is 1500. The identity GCD × LCM = 500 × 12 = 6000 checks both results.
Work through GCF and LCMQuestions about 500
What are the factors of 500?
The positive factors are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500. There are 12 factors, including 1 and 500.
Is 500 a prime number?
No. 500 is composite: 2^2 × 5^3 = 500.
How do you write 500 in Roman numerals?
500 is D in standard subtractive Roman numeral notation.
What is the binary representation of 500?
500 in decimal is 111110100 in base 2. Adding its active place values gives 256 + 128 + 64 + 32 + 16 + 4 = 500.
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 500
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 500 add to 5. 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.