2013
2013 is a odd composite number that follows 2012 and precedes 2014. It is composed of 8 distinct factors: 1, 3, 11, 33, 61, 183, 671, 2013. Its prime factorization can be written as 3 × 11 × 61. 2013 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2013 is represented as 11111011101 in binary and 7DD in hexadecimal. Historically, it is written as MMXIII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 11 × 61) reveals 3 prime building blocks.
Divisible by 2
2013 ends in 3, so it is odd.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
2013 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 6 is not a multiple of 9.
Divisible by 10
2013 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 2013 within several notable number theory sequences:
Timeline
Deep dive
How 2013 breaks down
2013 carries 8 distinct factors and a digit signature of 6 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 963, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11111011101 supports bitwise reasoning, hexadecimal 7DD aligns with computing notation, and the Roman numeral MMXIII keeps the encyclopedic tradition alive. These attributes make 2013 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2013 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2008–2018) to tune search ranges, and educators feature 2013 in worksheets about factor trees. Its binary footprint of length 11 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 2013 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 2013
Is 2013 a prime number?
2013 is composite with 8 total factors and the prime factorization 3 × 11 × 61.
What is the prime factorization of 2013?
It breaks down as 3 × 11 × 61, multiplying the primes 3 × 11 × 61.
How is 2013 represented in binary and hexadecimal?
2013 converts to 11111011101 in binary and 7DD in hexadecimal, which are helpful for computer science applications.
Is 2013 a perfect square, cube, or triangular number?
2013 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2013?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.