409
409 is a odd prime number that follows 408 and precedes 410. As a prime number, 409 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 409. 409 is classified as a deficient number based on the sum of its proper divisors. In computer science, 409 is represented as 110011001 in binary and 199 in hexadecimal. Historically, it is written as CDIX in Roman numerals.
Factor Analysis
2 FactorsProperties
409 is prime, so its only factors are 1 and 409.
Divisible by 2
409 ends in 9, so it is odd.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 09 are not divisible by 4.
Divisible by 5
409 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 13 is not a multiple of 9.
Divisible by 10
409 does not end in 0.
Divisible by 11
The alternating digit sum 13 is not a multiple of 11.
Deficient classification and digit analytics place 409 within several notable number theory sequences:
Timeline
Deep dive
How 409 breaks down
409 carries 2 distinct factors and a digit signature of 13 (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 110011001 supports bitwise reasoning, hexadecimal 199 aligns with computing notation, and the Roman numeral CDIX keeps the encyclopedic tradition alive. These attributes make 409 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 409 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (404–414) to tune search ranges, and educators feature 409 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 409 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 409
Is 409 a prime number?
409 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 409?
409 is already prime, so the factorization is simply 409.
How is 409 represented in binary and hexadecimal?
409 converts to 110011001 in binary and 199 in hexadecimal, which are helpful for computer science applications.
Is 409 a perfect square, cube, or triangular number?
409 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 409?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.