413
413 is a odd composite number that follows 412 and precedes 414. It is composed of 4 distinct factors: 1, 7, 59, 413. Its prime factorization can be written as 7 × 59. 413 is classified as a deficient number based on the sum of its proper divisors. In computer science, 413 is represented as 110011101 in binary and 19D in hexadecimal. Historically, it is written as CDXIII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (7 × 59) reveals 2 prime building blocks.
Divisible by 2
413 ends in 3, so it is odd.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
413 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 8 is not a multiple of 9.
Divisible by 10
413 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 413 within several notable number theory sequences:
Timeline
Deep dive
How 413 breaks down
413 carries 4 distinct factors and a digit signature of 8 (8 as the digital root). The deficient classification indicates that its proper divisors sum to 67, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110011101 supports bitwise reasoning, hexadecimal 19D aligns with computing notation, and the Roman numeral CDXIII keeps the encyclopedic tradition alive. These attributes make 413 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 413 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (408–418) to tune search ranges, and educators feature 413 in worksheets about factor trees. Its binary footprint of length 9 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 413 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 413
Is 413 a prime number?
413 is composite with 4 total factors and the prime factorization 7 × 59.
What is the prime factorization of 413?
It breaks down as 7 × 59, multiplying the primes 7 × 59.
How is 413 represented in binary and hexadecimal?
413 converts to 110011101 in binary and 19D in hexadecimal, which are helpful for computer science applications.
Is 413 a perfect square, cube, or triangular number?
413 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 413?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.