Number dictionary · Exact arithmetic
520: factors and number facts
five hundred twenty is an even number and is composite. Its 16 positive divisors form 8 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- five hundred twenty
- Roman numeral
- DXX
- Prime factorization
- 2^3 × 5 × 13
- Digital root
- 7
All factors of 520
A positive factor divides 520 with no remainder. In ascending order, the complete list is:
1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
Factor pairs
- 1 × 520 = 520
- 2 × 260 = 520
- 4 × 130 = 520
- 5 × 104 = 520
- 8 × 65 = 520
- 10 × 52 = 520
- 13 × 40 = 520
- 20 × 26 = 520
Each pair describes an arrangement of 520 items into equal rows. The pairs have different row and column counts; 520 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 16
- Sum of all divisors
- 1260
- Sum excluding 520
- 740
- Classification
- abundant
520 is abundant because its proper divisors add to 740, which is greater than 520.
Prime factorization of 520
520 = 2^3 × 5 × 13
Repeated division, step by step
- 520 ÷ 2 = 260
- 260 ÷ 2 = 130
- 130 ÷ 2 = 65
- 65 ÷ 5 = 13
- 13 ÷ 13 = 1
Multiply the prime divisors in these steps to reconstruct 520. An exponent records how many times the same prime occurs. The divisor-count calculation is (3 + 1) × (1 + 1) × (1 + 1) = 16.
The preceding prime is 509. The next larger prime is 521. The factor list above explains why 520 is composite.
Learn the factorization method520 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | five hundred twenty |
| Roman numeral | DXX |
| Binary (base 2) | 1000001000 |
| Octal (base 8) | 1010 |
| Decimal (base 10) | 520 |
| Hexadecimal (base 16) | 208 |
Check the binary conversion
Read 1000001000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
512 + 8 = 520
Check the hexadecimal conversion
2 × 16^2 + 0 × 16^1 + 8 × 16^0 = 520
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 520
- 520 squared
- 520 × 520 = 270,400
- 520 cubed
- 520 × 520 × 520 = 140,608,000
- Square root
- ≈ 22.803509
- Simplified radical
- 2√130
520 lies between 484 (22²) and 529 (23²), so it is not a perfect square. It is not a perfect cube.
520 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 520.
Distinguish a square from a square rootMultiplication table for 520
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 | 260 | 0 | Yes |
| 3 | 173 | 1 | No |
| 4 | 130 | 0 | Yes |
| 5 | 104 | 0 | Yes |
| 6 | 86 | 4 | No |
| 7 | 74 | 2 | No |
| 8 | 65 | 0 | Yes |
| 9 | 57 | 7 | No |
| 10 | 52 | 0 | Yes |
| 11 | 47 | 3 | No |
| 12 | 43 | 4 | No |
For example, 520 = 7 × 74 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 520
520 contains 3 decimal digits. Its digit sum is 5 + 2 + 0 = 7.
- 520: 5 + 2 + 0 = 7
The digital root is 7. Reversing its digits gives 025; 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, 520/100 simplifies to 26/5 by dividing both terms by their greatest common divisor, 20. Its decimal value is 5.2. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 520 and 12 is 4. Their least common multiple is 1560. The identity GCD × LCM = 520 × 12 = 6240 checks both results.
Work through GCF and LCMQuestions about 520
What are the factors of 520?
The positive factors are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520. There are 16 factors, including 1 and 520.
Is 520 a prime number?
No. 520 is composite: 2^3 × 5 × 13 = 520.
How do you write 520 in Roman numerals?
520 is DXX in standard subtractive Roman numeral notation.
What is the binary representation of 520?
520 in decimal is 1000001000 in base 2. Adding its active place values gives 512 + 8 = 520.
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 520
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 520 add to 7. 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.