Number dictionary · Exact arithmetic
231: factors and number facts
two hundred thirty-one is an odd number and is composite. Its 8 positive divisors form 4 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- two hundred thirty-one
- Roman numeral
- CCXXXI
- Prime factorization
- 3 × 7 × 11
- Digital root
- 6
All factors of 231
A positive factor divides 231 with no remainder. In ascending order, the complete list is:
1, 3, 7, 11, 21, 33, 77, 231
Factor pairs
- 1 × 231 = 231
- 3 × 77 = 231
- 7 × 33 = 231
- 11 × 21 = 231
Each pair describes an arrangement of 231 items into equal rows. The pairs have different row and column counts; 231 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 8
- Sum of all divisors
- 384
- Sum excluding 231
- 153
- Classification
- deficient
231 is deficient because its proper divisors add to 153, which is less than 231.
Prime factorization of 231
231 = 3 × 7 × 11
Repeated division, step by step
- 231 ÷ 3 = 77
- 77 ÷ 7 = 11
- 11 ÷ 11 = 1
Multiply the prime divisors in these steps to reconstruct 231. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) × (1 + 1) = 8.
The preceding prime is 229. The next larger prime is 233. The factor list above explains why 231 is composite.
Learn the factorization method231 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | two hundred thirty-one |
| Roman numeral | CCXXXI |
| Binary (base 2) | 11100111 |
| Octal (base 8) | 347 |
| Decimal (base 10) | 231 |
| Hexadecimal (base 16) | E7 |
Check the binary conversion
Read 11100111 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
128 + 64 + 32 + 4 + 2 + 1 = 231
Check the hexadecimal conversion
14 × 16^1 + 7 × 16^0 = 231
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 231
- 231 squared
- 231 × 231 = 53,361
- 231 cubed
- 231 × 231 × 231 = 12,326,391
- Square root
- ≈ 15.198684
- Simplified radical
- √231
231 lies between 225 (15²) and 256 (16²), so it is not a perfect square. It is not a perfect cube.
231 is triangular: it is the sum of the integers from 1 through 21.
Distinguish a square from a square rootMultiplication table for 231
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 | 115 | 1 | No |
| 3 | 77 | 0 | Yes |
| 4 | 57 | 3 | No |
| 5 | 46 | 1 | No |
| 6 | 38 | 3 | No |
| 7 | 33 | 0 | Yes |
| 8 | 28 | 7 | No |
| 9 | 25 | 6 | No |
| 10 | 23 | 1 | No |
| 11 | 21 | 0 | Yes |
| 12 | 19 | 3 | No |
For example, 231 = 7 × 33 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 231
231 contains 3 decimal digits. Its digit sum is 2 + 3 + 1 = 6.
- 231: 2 + 3 + 1 = 6
The digital root is 6. Reversing its digits gives 132; 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, 231/100 simplifies to 231/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 2.31. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 231 and 12 is 3. Their least common multiple is 924. The identity GCD × LCM = 231 × 12 = 2772 checks both results.
Work through GCF and LCMQuestions about 231
What are the factors of 231?
The positive factors are 1, 3, 7, 11, 21, 33, 77, 231. There are 8 factors, including 1 and 231.
Is 231 a prime number?
No. 231 is composite: 3 × 7 × 11 = 231.
How do you write 231 in Roman numerals?
231 is CCXXXI in standard subtractive Roman numeral notation.
What is the binary representation of 231?
231 in decimal is 11100111 in base 2. Adding its active place values gives 128 + 64 + 32 + 4 + 2 + 1 = 231.
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 231
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 231 add to 6. 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.