3408
3408 is a even composite number that follows 3407 and precedes 3409. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 71, 142, 213, 284, 426, 568, 852, 1136, 1704, 3408. Its prime factorization can be written as 2^4 × 3 × 71. 3408 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3408 is represented as 110101010000 in binary and D50 in hexadecimal. Historically, it is written as MMMCDVIII in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 71) reveals 6 prime building blocks.
Divisible by 2
3408 ends in 8, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
3408 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 15 is not a multiple of 9.
Divisible by 10
3408 does not end in 0.
Divisible by 11
The alternating digit sum -9 is not a multiple of 11.
Abundant classification and digit analytics place 3408 within several notable number theory sequences:
Timeline
Deep dive
How 3408 breaks down
3408 carries 20 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 5520, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110101010000 supports bitwise reasoning, hexadecimal D50 aligns with computing notation, and the Roman numeral MMMCDVIII keeps the encyclopedic tradition alive. These attributes make 3408 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3408 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3403–3413) to tune search ranges, and educators feature 3408 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 3408 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 3408
Is 3408 a prime number?
3408 is composite with 20 total factors and the prime factorization 2^4 × 3 × 71.
What is the prime factorization of 3408?
It breaks down as 2^4 × 3 × 71, multiplying the primes 2 × 2 × 2 × 2 × 3 × 71.
How is 3408 represented in binary and hexadecimal?
3408 converts to 110101010000 in binary and D50 in hexadecimal, which are helpful for computer science applications.
Is 3408 a perfect square, cube, or triangular number?
3408 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3408?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.