Number dictionary · Exact arithmetic
321: factors and number facts
three hundred twenty-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 twenty-one
- Roman numeral
- CCCXXI
- Prime factorization
- 3 × 107
- Digital root
- 6
All factors of 321
A positive factor divides 321 with no remainder. In ascending order, the complete list is:
1, 3, 107, 321
Factor pairs
- 1 × 321 = 321
- 3 × 107 = 321
Each pair describes an arrangement of 321 items into equal rows. The pairs have different row and column counts; 321 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 4
- Sum of all divisors
- 432
- Sum excluding 321
- 111
- Classification
- deficient
321 is deficient because its proper divisors add to 111, which is less than 321.
Prime factorization of 321
321 = 3 × 107
Repeated division, step by step
- 321 ÷ 3 = 107
- 107 ÷ 107 = 1
Multiply the prime divisors in these steps to reconstruct 321. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) × (1 + 1) = 4.
The preceding prime is 317. The next larger prime is 331. The factor list above explains why 321 is composite.
Learn the factorization method321 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three hundred twenty-one |
| Roman numeral | CCCXXI |
| Binary (base 2) | 101000001 |
| Octal (base 8) | 501 |
| Decimal (base 10) | 321 |
| Hexadecimal (base 16) | 141 |
Check the binary conversion
Read 101000001 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 + 1 = 321
Check the hexadecimal conversion
1 × 16^2 + 4 × 16^1 + 1 × 16^0 = 321
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 321
- 321 squared
- 321 × 321 = 103,041
- 321 cubed
- 321 × 321 × 321 = 33,076,161
- Square root
- ≈ 17.916473
- Simplified radical
- √321
321 lies between 289 (17²) and 324 (18²), so it is not a perfect square. It is not a perfect cube.
321 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 321.
Distinguish a square from a square rootMultiplication table for 321
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 | 1 | No |
| 3 | 107 | 0 | Yes |
| 4 | 80 | 1 | No |
| 5 | 64 | 1 | No |
| 6 | 53 | 3 | No |
| 7 | 45 | 6 | No |
| 8 | 40 | 1 | No |
| 9 | 35 | 6 | No |
| 10 | 32 | 1 | No |
| 11 | 29 | 2 | No |
| 12 | 26 | 9 | No |
For example, 321 = 7 × 45 + 6. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 321
321 contains 3 decimal digits. Its digit sum is 3 + 2 + 1 = 6.
- 321: 3 + 2 + 1 = 6
The digital root is 6. Reversing its digits gives 123; 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, 321/100 simplifies to 321/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 3.21. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 321 and 12 is 3. Their least common multiple is 1284. The identity GCD × LCM = 321 × 12 = 3852 checks both results.
Work through GCF and LCMQuestions about 321
What are the factors of 321?
The positive factors are 1, 3, 107, 321. There are 4 factors, including 1 and 321.
Is 321 a prime number?
No. 321 is composite: 3 × 107 = 321.
How do you write 321 in Roman numerals?
321 is CCCXXI in standard subtractive Roman numeral notation.
What is the binary representation of 321?
321 in decimal is 101000001 in base 2. Adding its active place values gives 256 + 64 + 1 = 321.
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 321
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 321 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.