13
13 is a odd prime number that follows 12 and precedes 14. As a prime number, 13 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 13. 13 is classified as a deficient number based on the sum of its proper divisors. In computer science, 13 is represented as 1101 in binary and D in hexadecimal. Historically, it is written as XIII in Roman numerals. It also belongs to the Fibonacci number sequence.
Factor Analysis
2 FactorsProperties
13 is prime, so its only factors are 1 and 13.
Divisible by 2
13 ends in 3, so it is odd.
Divisible by 3
The digit sum 4 is not a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
13 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 4 is not a multiple of 9.
Divisible by 10
13 does not end in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Deficient classification and digit analytics place 13 within several notable number theory sequences:
Timeline
Deep dive
How 13 breaks down
13 carries 2 distinct factors and a digit signature of 4 (4 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 1101 supports bitwise reasoning, hexadecimal D aligns with computing notation, and the Roman numeral XIII keeps the encyclopedic tradition alive. These attributes make 13 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 13 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8–18) to tune search ranges, and educators feature 13 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, Fibonacci numbers) help historians, numerologists, and trivia writers tie 13 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 13
Is 13 a prime number?
13 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 13?
13 is already prime, so the factorization is simply 13.
How is 13 represented in binary and hexadecimal?
13 converts to 1101 in binary and D in hexadecimal, which are helpful for computer science applications.
Is 13 a perfect square, cube, or triangular number?
13 is not a perfect square, is not a perfect cube, and is not triangular. It also belongs to the Fibonacci sequence.
What are the digit sum and digital root of 13?
The digits sum to 4, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.