Number dictionary · Exact arithmetic
504: factors and number facts
five hundred four is an even number and is composite. Its 24 positive divisors form 12 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- five hundred four
- Roman numeral
- DIV
- Prime factorization
- 2^3 × 3^2 × 7
- Digital root
- 9
All factors of 504
A positive factor divides 504 with no remainder. In ascending order, the complete list is:
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
Factor pairs
- 1 × 504 = 504
- 2 × 252 = 504
- 3 × 168 = 504
- 4 × 126 = 504
- 6 × 84 = 504
- 7 × 72 = 504
- 8 × 63 = 504
- 9 × 56 = 504
- 12 × 42 = 504
- 14 × 36 = 504
- 18 × 28 = 504
- 21 × 24 = 504
Each pair describes an arrangement of 504 items into equal rows. The pairs have different row and column counts; 504 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 24
- Sum of all divisors
- 1560
- Sum excluding 504
- 1056
- Classification
- abundant
504 is abundant because its proper divisors add to 1056, which is greater than 504.
Prime factorization of 504
504 = 2^3 × 3^2 × 7
Repeated division, step by step
- 504 ÷ 2 = 252
- 252 ÷ 2 = 126
- 126 ÷ 2 = 63
- 63 ÷ 3 = 21
- 21 ÷ 3 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 504. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (2 + 1) × (1 + 1) = 24.
The preceding prime is 503. The next larger prime is 509. The factor list above explains why 504 is composite.
Learn the factorization method504 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | five hundred four |
| Roman numeral | DIV |
| Binary (base 2) | 111111000 |
| Octal (base 8) | 770 |
| Decimal (base 10) | 504 |
| Hexadecimal (base 16) | 1F8 |
Check the binary conversion
Read 111111000 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 = 504
Check the hexadecimal conversion
1 × 16^2 + 15 × 16^1 + 8 × 16^0 = 504
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 504
- 504 squared
- 504 × 504 = 254,016
- 504 cubed
- 504 × 504 × 504 = 128,024,064
- Square root
- ≈ 22.449944
- Simplified radical
- 6√14
504 lies between 484 (22²) and 529 (23²), so it is not a perfect square. It is not a perfect cube.
504 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 504.
Distinguish a square from a square rootMultiplication table for 504
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 | 252 | 0 | Yes |
| 3 | 168 | 0 | Yes |
| 4 | 126 | 0 | Yes |
| 5 | 100 | 4 | No |
| 6 | 84 | 0 | Yes |
| 7 | 72 | 0 | Yes |
| 8 | 63 | 0 | Yes |
| 9 | 56 | 0 | Yes |
| 10 | 50 | 4 | No |
| 11 | 45 | 9 | No |
| 12 | 42 | 0 | Yes |
For example, 504 = 7 × 72 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 504
504 contains 3 decimal digits. Its digit sum is 5 + 0 + 4 = 9.
- 504: 5 + 0 + 4 = 9
The digital root is 9. Reversing its digits gives 405; 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, 504/100 simplifies to 126/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 5.04. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 504 and 12 is 12. Their least common multiple is 504. The identity GCD × LCM = 504 × 12 = 6048 checks both results.
Work through GCF and LCMQuestions about 504
What are the factors of 504?
The positive factors are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504. There are 24 factors, including 1 and 504.
Is 504 a prime number?
No. 504 is composite: 2^3 × 3^2 × 7 = 504.
How do you write 504 in Roman numerals?
504 is DIV in standard subtractive Roman numeral notation.
What is the binary representation of 504?
504 in decimal is 111111000 in base 2. Adding its active place values gives 256 + 128 + 64 + 32 + 16 + 8 = 504.
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 504
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 504 add to 9. 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.