408
408 is a even composite number that follows 407 and precedes 409. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. Its prime factorization can be written as 2^3 × 3 × 17. 408 is classified as a abundant number based on the sum of its proper divisors. In computer science, 408 is represented as 110011000 in binary and 198 in hexadecimal. Historically, it is written as CDVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 17) reveals 5 prime building blocks.
Divisible by 2
408 ends in 8, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
408 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 12 is not a multiple of 9.
Divisible by 10
408 does not end in 0.
Divisible by 11
The alternating digit sum 12 is not a multiple of 11.
Abundant classification and digit analytics place 408 within several notable number theory sequences:
Timeline
Deep dive
How 408 breaks down
408 carries 16 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 672, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110011000 supports bitwise reasoning, hexadecimal 198 aligns with computing notation, and the Roman numeral CDVIII keeps the encyclopedic tradition alive. These attributes make 408 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 408 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (403–413) to tune search ranges, and educators feature 408 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, Abundant numbers) help historians, numerologists, and trivia writers tie 408 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 408
Is 408 a prime number?
408 is composite with 16 total factors and the prime factorization 2^3 × 3 × 17.
What is the prime factorization of 408?
It breaks down as 2^3 × 3 × 17, multiplying the primes 2 × 2 × 2 × 3 × 17.
How is 408 represented in binary and hexadecimal?
408 converts to 110011000 in binary and 198 in hexadecimal, which are helpful for computer science applications.
Is 408 a perfect square, cube, or triangular number?
408 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 408?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.