1728
1728 is a even composite number that follows 1727 and precedes 1729. It is composed of 28 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728. Its prime factorization can be written as 2^6 × 3^3. 1728 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1728 is represented as 11011000000 in binary and 6C0 in hexadecimal. Historically, it is written as MDCCXXVIII in Roman numerals. It also belongs to the perfect cube sequence.
Factor Analysis
28 FactorsProperties
The prime factorization (2^6 × 3^3) reveals 9 prime building blocks.
Divisible by 2
1728 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
1728 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 18 is a multiple of 9.
Divisible by 10
1728 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 1728 within several notable number theory sequences:
Timeline
Deep dive
How 1728 breaks down
1728 carries 28 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 3352, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011000000 supports bitwise reasoning, hexadecimal 6C0 aligns with computing notation, and the Roman numeral MDCCXXVIII keeps the encyclopedic tradition alive. These attributes make 1728 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1728 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1723–1733) to tune search ranges, and educators feature 1728 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, Perfect cubes) help historians, numerologists, and trivia writers tie 1728 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 1728
Is 1728 a prime number?
1728 is composite with 28 total factors and the prime factorization 2^6 × 3^3.
What is the prime factorization of 1728?
It breaks down as 2^6 × 3^3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3.
How is 1728 represented in binary and hexadecimal?
1728 converts to 11011000000 in binary and 6C0 in hexadecimal, which are helpful for computer science applications.
Is 1728 a perfect square, cube, or triangular number?
1728 is not a perfect square, is a perfect cube, and is not triangular.
What are the digit sum and digital root of 1728?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.