Number dictionary · Exact arithmetic
507: factors and number facts
five hundred seven is an odd number and is composite. Its 6 positive divisors form 3 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- five hundred seven
- Roman numeral
- DVII
- Prime factorization
- 3 × 13^2
- Digital root
- 3
All factors of 507
A positive factor divides 507 with no remainder. In ascending order, the complete list is:
1, 3, 13, 39, 169, 507
Factor pairs
- 1 × 507 = 507
- 3 × 169 = 507
- 13 × 39 = 507
Each pair describes an arrangement of 507 items into equal rows. The pairs have different row and column counts; 507 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 6
- Sum of all divisors
- 732
- Sum excluding 507
- 225
- Classification
- deficient
507 is deficient because its proper divisors add to 225, which is less than 507.
Prime factorization of 507
507 = 3 × 13^2
Repeated division, step by step
- 507 ÷ 3 = 169
- 169 ÷ 13 = 13
- 13 ÷ 13 = 1
Multiply the prime divisors in these steps to reconstruct 507. An exponent records how many times the same prime occurs. The divisor-count calculation is (1 + 1) × (2 + 1) = 6.
The preceding prime is 503. The next larger prime is 509. The factor list above explains why 507 is composite.
Learn the factorization method507 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | five hundred seven |
| Roman numeral | DVII |
| Binary (base 2) | 111111011 |
| Octal (base 8) | 773 |
| Decimal (base 10) | 507 |
| Hexadecimal (base 16) | 1FB |
Check the binary conversion
Read 111111011 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 + 2 + 1 = 507
Check the hexadecimal conversion
1 × 16^2 + 15 × 16^1 + 11 × 16^0 = 507
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 507
- 507 squared
- 507 × 507 = 257,049
- 507 cubed
- 507 × 507 × 507 = 130,323,843
- Square root
- ≈ 22.516660
- Simplified radical
- 13√3
507 lies between 484 (22²) and 529 (23²), so it is not a perfect square. It is not a perfect cube.
507 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 507.
Distinguish a square from a square rootMultiplication table for 507
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 | 253 | 1 | No |
| 3 | 169 | 0 | Yes |
| 4 | 126 | 3 | No |
| 5 | 101 | 2 | No |
| 6 | 84 | 3 | No |
| 7 | 72 | 3 | No |
| 8 | 63 | 3 | No |
| 9 | 56 | 3 | No |
| 10 | 50 | 7 | No |
| 11 | 46 | 1 | No |
| 12 | 42 | 3 | No |
For example, 507 = 7 × 72 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 507
507 contains 3 decimal digits. Its digit sum is 5 + 0 + 7 = 12.
- 507: 5 + 0 + 7 = 12
- 12: 1 + 2 = 3
The digital root is 3. Reversing its digits gives 705; 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, 507/100 simplifies to 507/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 5.07. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 507 and 12 is 3. Their least common multiple is 2028. The identity GCD × LCM = 507 × 12 = 6084 checks both results.
Work through GCF and LCMQuestions about 507
What are the factors of 507?
The positive factors are 1, 3, 13, 39, 169, 507. There are 6 factors, including 1 and 507.
Is 507 a prime number?
No. 507 is composite: 3 × 13^2 = 507.
How do you write 507 in Roman numerals?
507 is DVII in standard subtractive Roman numeral notation.
What is the binary representation of 507?
507 in decimal is 111111011 in base 2. Adding its active place values gives 256 + 128 + 64 + 32 + 16 + 8 + 2 + 1 = 507.
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 507
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 507 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.