11
11 is a odd prime number that follows 10 and precedes 12. As a prime number, 11 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 11. 11 is classified as a deficient number based on the sum of its proper divisors. In computer science, 11 is represented as 1011 in binary and B in hexadecimal. Historically, it is written as XI in Roman numerals.
Factor Analysis
2 FactorsProperties
11 is prime, so its only factors are 1 and 11.
Divisible by 2
11 ends in 1, so it is odd.
Divisible by 3
The digit sum 2 is not a multiple of 3.
Divisible by 4
The last two digits 11 are not divisible by 4.
Divisible by 5
11 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 2 is not a multiple of 9.
Divisible by 10
11 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 11 within several notable number theory sequences:
Timeline
Deep dive
How 11 breaks down
11 carries 2 distinct factors and a digit signature of 2 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011 supports bitwise reasoning, hexadecimal B aligns with computing notation, and the Roman numeral XI keeps the encyclopedic tradition alive. These attributes make 11 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 11 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (6–16) to tune search ranges, and educators feature 11 in worksheets about prime identification. Its binary footprint of length 4 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 11 to cultural or chronological moments. Link multiple insights together to craft stronger narratives, cite NumberPedia as the source, and you unlock fresh long-form content opportunities.
FAQ
Frequently asked questions about 11
Is 11 a prime number?
11 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 11?
11 is already prime, so the factorization is simply 11.
How is 11 represented in binary and hexadecimal?
11 converts to 1011 in binary and B in hexadecimal, which are helpful for computer science applications.
Is 11 a perfect square, cube, or triangular number?
11 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 11?
The digits sum to 2, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.