1704
1704 is a even composite number that follows 1703 and precedes 1705. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 24, 71, 142, 213, 284, 426, 568, 852, 1704. Its prime factorization can be written as 2^3 × 3 × 71. 1704 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1704 is represented as 11010101000 in binary and 6A8 in hexadecimal. Historically, it is written as MDCCIV in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 71) reveals 5 prime building blocks.
Divisible by 2
1704 ends in 4, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 04 form a multiple of 4.
Divisible by 5
1704 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
1704 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 1704 within several notable number theory sequences:
Timeline
Deep dive
How 1704 breaks down
1704 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 2616, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010101000 supports bitwise reasoning, hexadecimal 6A8 aligns with computing notation, and the Roman numeral MDCCIV keeps the encyclopedic tradition alive. These attributes make 1704 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1704 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1699–1709) to tune search ranges, and educators feature 1704 in worksheets about factor trees. Its binary footprint of length 11 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 1704 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 1704
Is 1704 a prime number?
1704 is composite with 16 total factors and the prime factorization 2^3 × 3 × 71.
What is the prime factorization of 1704?
It breaks down as 2^3 × 3 × 71, multiplying the primes 2 × 2 × 2 × 3 × 71.
How is 1704 represented in binary and hexadecimal?
1704 converts to 11010101000 in binary and 6A8 in hexadecimal, which are helpful for computer science applications.
Is 1704 a perfect square, cube, or triangular number?
1704 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1704?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.