2728
2728 is a even composite number that follows 2727 and precedes 2729. It is composed of 16 distinct factors: 1, 2, 4, 8, 11, 22, 31, 44, 62, 88, 124, 248, 341, 682, 1364, 2728. Its prime factorization can be written as 2^3 × 11 × 31. 2728 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2728 is represented as 101010101000 in binary and AA8 in hexadecimal. Historically, it is written as MMDCCXXVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 11 × 31) reveals 5 prime building blocks.
Divisible by 2
2728 ends in 8, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
2728 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 19 is not a multiple of 9.
Divisible by 10
2728 does not end in 0.
Divisible by 11
The alternating digit sum -11 is a multiple of 11.
Abundant classification and digit analytics place 2728 within several notable number theory sequences:
Timeline
Deep dive
How 2728 breaks down
2728 carries 16 distinct factors and a digit signature of 19 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 3032, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101010101000 supports bitwise reasoning, hexadecimal AA8 aligns with computing notation, and the Roman numeral MMDCCXXVIII keeps the encyclopedic tradition alive. These attributes make 2728 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2728 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2723–2733) to tune search ranges, and educators feature 2728 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 2728 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 2728
Is 2728 a prime number?
2728 is composite with 16 total factors and the prime factorization 2^3 × 11 × 31.
What is the prime factorization of 2728?
It breaks down as 2^3 × 11 × 31, multiplying the primes 2 × 2 × 2 × 11 × 31.
How is 2728 represented in binary and hexadecimal?
2728 converts to 101010101000 in binary and AA8 in hexadecimal, which are helpful for computer science applications.
Is 2728 a perfect square, cube, or triangular number?
2728 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2728?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.