Number dictionary · Exact arithmetic
391: factors and number facts
three hundred ninety-one is an odd number and is composite. Its 4 positive divisors form 2 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- three hundred ninety-one
- Roman numeral
- CCCXCI
- Prime factorization
- 17 × 23
- Digital root
- 4
All factors of 391
A positive factor divides 391 with no remainder. In ascending order, the complete list is:
1, 17, 23, 391
Factor pairs
- 1 × 391 = 391
- 17 × 23 = 391
Each pair describes an arrangement of 391 items into equal rows. The pairs have different row and column counts; 391 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 432
- Sum excluding 391
- 41
- Classification
- deficient
391 is deficient because its proper divisors add to 41, which is less than 391.
Prime factorization of 391
391 = 17 × 23
Repeated division, step by step
- 391 ÷ 17 = 23
- 23 ÷ 23 = 1
Multiply the prime divisors in these steps to reconstruct 391. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 389. The next larger prime is 397. The factor list above explains why 391 is composite.
Learn the factorization method391 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred ninety-one |
| Roman numeral | CCCXCI |
| Binary (base 2) | 110000111 |
| Octal (base 8) | 607 |
| Decimal (base 10) | 391 |
| Hexadecimal (base 16) | 187 |
Check the binary conversion
Read 110000111 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 + 4 + 2 + 1 = 391
Check the hexadecimal conversion
1 × 16^2 + 8 × 16^1 + 7 × 16^0 = 391
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 391
- 391 squared
- 391 × 391 = 152,881
- 391 cubed
- 391 × 391 × 391 = 59,776,471
- Square root
- ≈ 19.773720
- Simplified radical
- √391
391 lies between 361 (19²) and 400 (20²), so it is not a perfect square. It is not a perfect cube.
391 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 391.
Distinguish a square from a square rootMultiplication table for 391
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 | 195 | 1 | No |
| 3 | 130 | 1 | No |
| 4 | 97 | 3 | No |
| 5 | 78 | 1 | No |
| 6 | 65 | 1 | No |
| 7 | 55 | 6 | No |
| 8 | 48 | 7 | No |
| 9 | 43 | 4 | No |
| 10 | 39 | 1 | No |
| 11 | 35 | 6 | No |
| 12 | 32 | 7 | No |
For example, 391 = 7 × 55 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 391
391 contains 3 decimal digits. Its digit sum is 3 + 9 + 1 = 13.
- 391: 3 + 9 + 1 = 13
- 13: 1 + 3 = 4
The digital root is 4. Reversing its digits gives 193; 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, 391/100 simplifies to 391/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 3.91. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 391 and 12 is 1. Their least common multiple is 4692. The identity GCD × LCM = 391 × 12 = 4692 checks both results.
Work through GCF and LCMQuestions about 391
What are the factors of 391?
The positive factors are 1, 17, 23, 391. There are 4 factors, including 1 and 391.
Is 391 a prime number?
No. 391 is composite: 17 × 23 = 391.
How do you write 391 in Roman numerals?
391 is CCCXCI in standard subtractive Roman numeral notation.
What is the binary representation of 391?
391 in decimal is 110000111 in base 2. Adding its active place values gives 256 + 128 + 4 + 2 + 1 = 391.
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 391
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 391 add to 13. 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.