Number dictionary · Exact arithmetic
3: factors and number facts
three 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
- Roman numeral
- III
- Prime factorization
- 3
- Digital root
- 3
All factors of 3
A positive factor divides 3 with no remainder. In ascending order, the complete list is:
1, 3
Factor pairs
- 1 × 3 = 3
Each pair describes an arrangement of 3 items into equal rows. The pairs have different row and column counts; 3 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 4
- Sum excluding 3
- 1
- Classification
- deficient
3 is deficient because its proper divisors add to 1, which is less than 3.
Prime factorization of 3
3 = 3
Repeated division, step by step
- 3 ÷ 3 = 1
Multiply the prime divisors in these steps to reconstruct 3. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 2. The next larger prime is 5. To check 3 for primality, it is sufficient to test possible divisors from 2 through 1 (there are no candidates in that interval).
Learn the factorization method3 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | three |
| Roman numeral | III |
| Binary (base 2) | 11 |
| Octal (base 8) | 3 |
| Decimal (base 10) | 3 |
| Hexadecimal (base 16) | 3 |
Check the binary conversion
Read 11 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
2 + 1 = 3
Check the hexadecimal conversion
3 × 16^0 = 3
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 3
- 3 squared
- 3 × 3 = 9
- 3 cubed
- 3 × 3 × 3 = 27
- Square root
- ≈ 1.732051
- Simplified radical
- √3
3 lies between 1 (1²) and 4 (2²), so it is not a perfect square. It is not a perfect cube.
3 is triangular: it is the sum of the integers from 1 through 2.
Distinguish a square from a square rootMultiplication table for 3
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 | 1 | 1 | No |
| 3 | 1 | 0 | Yes |
| 4 | 0 | 3 | No |
| 5 | 0 | 3 | No |
| 6 | 0 | 3 | No |
| 7 | 0 | 3 | No |
| 8 | 0 | 3 | No |
| 9 | 0 | 3 | No |
| 10 | 0 | 3 | No |
| 11 | 0 | 3 | No |
| 12 | 0 | 3 | No |
For example, 3 = 7 × 0 + 3. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 3
3 contains 1 decimal digit. Its digit sum is 3 = 3.
It already has one digit, so there is no reduction step.
The digital root is 3. 3 reads the same forward and backward, making it 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, 3/100 simplifies to 3/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 0.03.
The greatest common divisor of 3 and 12 is 3. Their least common multiple is 12. The identity GCD × LCM = 3 × 12 = 36 checks both results.
Work through GCF and LCMQuestions about 3
What are the factors of 3?
The positive factors are 1, 3. There are 2 factors, including 1 and 3.
Is 3 a prime number?
Yes. The only positive divisors of 3 are 1 and 3.
How do you write 3 in Roman numerals?
3 is III in standard subtractive Roman numeral notation.
What is the binary representation of 3?
3 in decimal is 11 in base 2. Adding its active place values gives 2 + 1 = 3.
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.