Number dictionary · Exact arithmetic
11: factors and number facts
eleven 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
- eleven
- Roman numeral
- XI
- Prime factorization
- 11
- Digital root
- 2
All factors of 11
A positive factor divides 11 with no remainder. In ascending order, the complete list is:
1, 11
Factor pairs
- 1 × 11 = 11
Each pair describes an arrangement of 11 items into equal rows. The pairs have different row and column counts; 11 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 2
- Sum of all divisors
- 12
- Sum excluding 11
- 1
- Classification
- deficient
11 is deficient because its proper divisors add to 1, which is less than 11.
Prime factorization of 11
11 = 11
Repeated division, step by step
- 11 ÷ 11 = 1
Multiply the prime divisors in these steps to reconstruct 11. Each prime in this factorization occurs once. The divisor-count calculation is (1 + 1) = 2.
The preceding prime is 7. The next larger prime is 13. To check 11 for primality, it is sufficient to test possible divisors from 2 through 3.
Learn the factorization method11 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | eleven |
| Roman numeral | XI |
| Binary (base 2) | 1011 |
| Octal (base 8) | 13 |
| Decimal (base 10) | 11 |
| Hexadecimal (base 16) | B |
Check the binary conversion
Read 1011 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
8 + 2 + 1 = 11
Check the hexadecimal conversion
11 × 16^0 = 11
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 11
- 11 squared
- 11 × 11 = 121
- 11 cubed
- 11 × 11 × 11 = 1,331
- Square root
- ≈ 3.316625
- Simplified radical
- √11
11 lies between 9 (3²) and 16 (4²), so it is not a perfect square. It is not a perfect cube.
11 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 11.
Distinguish a square from a square rootMultiplication table for 11
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 | 5 | 1 | No |
| 3 | 3 | 2 | No |
| 4 | 2 | 3 | No |
| 5 | 2 | 1 | No |
| 6 | 1 | 5 | No |
| 7 | 1 | 4 | No |
| 8 | 1 | 3 | No |
| 9 | 1 | 2 | No |
| 10 | 1 | 1 | No |
| 11 | 1 | 0 | Yes |
| 12 | 0 | 11 | No |
For example, 11 = 7 × 1 + 4. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 11
11 contains 2 decimal digits. Its digit sum is 1 + 1 = 2.
- 11: 1 + 1 = 2
The digital root is 2. 11 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, 11/100 simplifies to 11/100 by dividing both terms by their greatest common divisor, 1. Its decimal value is 0.11.
The greatest common divisor of 11 and 12 is 1. Their least common multiple is 132. The identity GCD × LCM = 11 × 12 = 132 checks both results.
Work through GCF and LCMQuestions about 11
What are the factors of 11?
The positive factors are 1, 11. There are 2 factors, including 1 and 11.
Is 11 a prime number?
Yes. The only positive divisors of 11 are 1 and 11.
How do you write 11 in Roman numerals?
11 is XI in standard subtractive Roman numeral notation.
What is the binary representation of 11?
11 in decimal is 1011 in base 2. Adding its active place values gives 8 + 2 + 1 = 11.
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 11
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 11 add to 2. 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.