613
613 is a odd prime number that follows 612 and precedes 614. As a prime number, 613 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 613. 613 is classified as a deficient number based on the sum of its proper divisors. In computer science, 613 is represented as 1001100101 in binary and 265 in hexadecimal. Historically, it is written as DCXIII in Roman numerals.
Factor Analysis
2 FactorsProperties
613 is prime, so its only factors are 1 and 613.
Divisible by 2
613 ends in 3, so it is odd.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
613 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 10 is not a multiple of 9.
Divisible by 10
613 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Deficient classification and digit analytics place 613 within several notable number theory sequences:
Timeline
Deep dive
How 613 breaks down
613 carries 2 distinct factors and a digit signature of 10 (1 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 1001100101 supports bitwise reasoning, hexadecimal 265 aligns with computing notation, and the Roman numeral DCXIII keeps the encyclopedic tradition alive. These attributes make 613 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 613 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (608–618) to tune search ranges, and educators feature 613 in worksheets about prime identification. Its binary footprint of length 10 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 613 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 613
Is 613 a prime number?
613 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 613?
613 is already prime, so the factorization is simply 613.
How is 613 represented in binary and hexadecimal?
613 converts to 1001100101 in binary and 265 in hexadecimal, which are helpful for computer science applications.
Is 613 a perfect square, cube, or triangular number?
613 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 613?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.