Number dictionary · Exact arithmetic
320: factors and number facts
three hundred twenty is an even number and is composite. Its 14 positive divisors form 7 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred twenty
- Roman numeral
- CCCXX
- Prime factorization
- 2^6 × 5
- Digital root
- 5
All factors of 320
A positive factor divides 320 with no remainder. In ascending order, the complete list is:
1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
Factor pairs
- 1 × 320 = 320
- 2 × 160 = 320
- 4 × 80 = 320
- 5 × 64 = 320
- 8 × 40 = 320
- 10 × 32 = 320
- 16 × 20 = 320
Each pair describes an arrangement of 320 items into equal rows. The pairs have different row and column counts; 320 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 14
- Sum of all divisors
- 762
- Sum excluding 320
- 442
- Classification
- abundant
320 is abundant because its proper divisors add to 442, which is greater than 320.
Prime factorization of 320
320 = 2^6 × 5
Repeated division, step by step
- 320 ÷ 2 = 160
- 160 ÷ 2 = 80
- 80 ÷ 2 = 40
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 ÷ 5 = 1
Multiply the prime divisors in these steps to reconstruct 320. An exponent records how many times the same prime occurs. The divisor-count calculation is (6 + 1) × (1 + 1) = 14.
The preceding prime is 317. The next larger prime is 331. The factor list above explains why 320 is composite.
Learn the factorization method320 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred twenty |
| Roman numeral | CCCXX |
| Binary (base 2) | 101000000 |
| Octal (base 8) | 500 |
| Decimal (base 10) | 320 |
| Hexadecimal (base 16) | 140 |
Check the binary conversion
Read 101000000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
256 + 64 = 320
Check the hexadecimal conversion
1 × 16^2 + 4 × 16^1 + 0 × 16^0 = 320
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 320
- 320 squared
- 320 × 320 = 102,400
- 320 cubed
- 320 × 320 × 320 = 32,768,000
- Square root
- ≈ 17.888544
- Simplified radical
- 8√5
320 lies between 289 (17²) and 324 (18²), so it is not a perfect square. It is not a perfect cube.
320 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 320.
Distinguish a square from a square rootMultiplication table for 320
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 | 160 | 0 | Yes |
| 3 | 106 | 2 | No |
| 4 | 80 | 0 | Yes |
| 5 | 64 | 0 | Yes |
| 6 | 53 | 2 | No |
| 7 | 45 | 5 | No |
| 8 | 40 | 0 | Yes |
| 9 | 35 | 5 | No |
| 10 | 32 | 0 | Yes |
| 11 | 29 | 1 | No |
| 12 | 26 | 8 | No |
For example, 320 = 7 × 45 + 5. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 320
320 contains 3 decimal digits. Its digit sum is 3 + 2 + 0 = 5.
- 320: 3 + 2 + 0 = 5
The digital root is 5. Reversing its digits gives 023; 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, 320/100 simplifies to 16/5 by dividing both terms by their greatest common divisor, 20. Its decimal value is 3.2. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 320 and 12 is 4. Their least common multiple is 960. The identity GCD × LCM = 320 × 12 = 3840 checks both results.
Work through GCF and LCMQuestions about 320
What are the factors of 320?
The positive factors are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320. There are 14 factors, including 1 and 320.
Is 320 a prime number?
No. 320 is composite: 2^6 × 5 = 320.
How do you write 320 in Roman numerals?
320 is CCCXX in standard subtractive Roman numeral notation.
What is the binary representation of 320?
320 in decimal is 101000000 in base 2. Adding its active place values gives 256 + 64 = 320.
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 320
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 320 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.