Number dictionary · Exact arithmetic
331: factors and number facts
three hundred thirty-one is an odd number and is prime. Its 2 positive divisors form 1 factor pair.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred thirty-one
- Roman numeral
- CCCXXXI
- Prime factorization
- 331
- Digital root
- 7
All factors of 331
A positive factor divides 331 with no remainder. In ascending order, the complete list is:
1, 331
Factor pairs
- 1 × 331 = 331
Each pair describes an arrangement of 331 items into equal rows. The pairs have different row and column counts; 331 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 332
- Sum excluding 331
- 1
- Classification
- deficient
331 is deficient because its proper divisors add to 1, which is less than 331.
Prime factorization of 331
331 = 331
Repeated division, step by step
- 331 ÷ 331 = 1
Multiply the prime divisors in these steps to reconstruct 331. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 317. The next larger prime is 337. To check 331 for primality, it is sufficient to test possible divisors from 2 through 18.
Learn the factorization method331 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred thirty-one |
| Roman numeral | CCCXXXI |
| Binary (base 2) | 101001011 |
| Octal (base 8) | 513 |
| Decimal (base 10) | 331 |
| Hexadecimal (base 16) | 14B |
Check the binary conversion
Read 101001011 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 + 8 + 2 + 1 = 331
Check the hexadecimal conversion
1 × 16^2 + 4 × 16^1 + 11 × 16^0 = 331
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 331
- 331 squared
- 331 × 331 = 109,561
- 331 cubed
- 331 × 331 × 331 = 36,264,691
- Square root
- ≈ 18.193405
- Simplified radical
- √331
331 lies between 324 (18²) and 361 (19²), so it is not a perfect square. It is not a perfect cube.
331 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 331.
Distinguish a square from a square rootMultiplication table for 331
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 | 165 | 1 | No |
| 3 | 110 | 1 | No |
| 4 | 82 | 3 | No |
| 5 | 66 | 1 | No |
| 6 | 55 | 1 | No |
| 7 | 47 | 2 | No |
| 8 | 41 | 3 | No |
| 9 | 36 | 7 | No |
| 10 | 33 | 1 | No |
| 11 | 30 | 1 | No |
| 12 | 27 | 7 | No |
For example, 331 = 7 × 47 + 2. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 331
331 contains 3 decimal digits. Its digit sum is 3 + 3 + 1 = 7.
- 331: 3 + 3 + 1 = 7
The digital root is 7. Reversing its digits gives 133; 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, 331/100 simplifies to 331/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 3.31. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 331 and 12 is 1. Their least common multiple is 3972. The identity GCD × LCM = 331 × 12 = 3972 checks both results.
Work through GCF and LCMQuestions about 331
What are the factors of 331?
The positive factors are 1, 331. There are 2 factors, including 1 and 331.
Is 331 a prime number?
Yes. The only positive divisors of 331 are 1 and 331.
How do you write 331 in Roman numerals?
331 is CCCXXXI in standard subtractive Roman numeral notation.
What is the binary representation of 331?
331 in decimal is 101001011 in base 2. Adding its active place values gives 256 + 64 + 8 + 2 + 1 = 331.
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 331
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 331 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.