2408
2408 is a even composite number that follows 2407 and precedes 2409. It is composed of 16 distinct factors: 1, 2, 4, 7, 8, 14, 28, 43, 56, 86, 172, 301, 344, 602, 1204, 2408. Its prime factorization can be written as 2^3 × 7 × 43. 2408 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2408 is represented as 100101101000 in binary and 968 in hexadecimal. Historically, it is written as MMCDVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 7 × 43) reveals 5 prime building blocks.
Divisible by 2
2408 ends in 8, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
2408 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 14 is not a multiple of 9.
Divisible by 10
2408 does not end in 0.
Divisible by 11
The alternating digit sum -10 is not a multiple of 11.
Abundant classification and digit analytics place 2408 within several notable number theory sequences:
Timeline
Deep dive
How 2408 breaks down
2408 carries 16 distinct factors and a digit signature of 14 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 2872, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100101101000 supports bitwise reasoning, hexadecimal 968 aligns with computing notation, and the Roman numeral MMCDVIII keeps the encyclopedic tradition alive. These attributes make 2408 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2408 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2403–2413) to tune search ranges, and educators feature 2408 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, Abundant numbers) help historians, numerologists, and trivia writers tie 2408 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 2408
Is 2408 a prime number?
2408 is composite with 16 total factors and the prime factorization 2^3 × 7 × 43.
What is the prime factorization of 2408?
It breaks down as 2^3 × 7 × 43, multiplying the primes 2 × 2 × 2 × 7 × 43.
How is 2408 represented in binary and hexadecimal?
2408 converts to 100101101000 in binary and 968 in hexadecimal, which are helpful for computer science applications.
Is 2408 a perfect square, cube, or triangular number?
2408 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2408?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.