2613
2613 is a odd composite number that follows 2612 and precedes 2614. It is composed of 8 distinct factors: 1, 3, 13, 39, 67, 201, 871, 2613. Its prime factorization can be written as 3 × 13 × 67. 2613 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2613 is represented as 101000110101 in binary and A35 in hexadecimal. Historically, it is written as MMDCXIII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 13 × 67) reveals 3 prime building blocks.
Divisible by 2
2613 ends in 3, so it is odd.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
2613 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 12 is not a multiple of 9.
Divisible by 10
2613 does not end in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Deficient classification and digit analytics place 2613 within several notable number theory sequences:
Timeline
Deep dive
How 2613 breaks down
2613 carries 8 distinct factors and a digit signature of 12 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 1195, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101000110101 supports bitwise reasoning, hexadecimal A35 aligns with computing notation, and the Roman numeral MMDCXIII keeps the encyclopedic tradition alive. These attributes make 2613 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2613 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2608–2618) to tune search ranges, and educators feature 2613 in worksheets about factor trees. Its binary footprint of length 12 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 2613 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 2613
Is 2613 a prime number?
2613 is composite with 8 total factors and the prime factorization 3 × 13 × 67.
What is the prime factorization of 2613?
It breaks down as 3 × 13 × 67, multiplying the primes 3 × 13 × 67.
How is 2613 represented in binary and hexadecimal?
2613 converts to 101000110101 in binary and A35 in hexadecimal, which are helpful for computer science applications.
Is 2613 a perfect square, cube, or triangular number?
2613 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2613?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.