1028
1028 is a even composite number that follows 1027 and precedes 1029. It is composed of 6 distinct factors: 1, 2, 4, 257, 514, 1028. Its prime factorization can be written as 2^2 × 257. 1028 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1028 is represented as 10000000100 in binary and 404 in hexadecimal. Historically, it is written as MXXVIII in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (2^2 × 257) reveals 3 prime building blocks.
Divisible by 2
1028 ends in 8, so it is even.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
1028 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 11 is not a multiple of 9.
Divisible by 10
1028 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Deficient classification and digit analytics place 1028 within several notable number theory sequences:
Timeline
Deep dive
How 1028 breaks down
1028 carries 6 distinct factors and a digit signature of 11 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 778, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000000100 supports bitwise reasoning, hexadecimal 404 aligns with computing notation, and the Roman numeral MXXVIII keeps the encyclopedic tradition alive. These attributes make 1028 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1028 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1023–1033) to tune search ranges, and educators feature 1028 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, Deficient numbers) help historians, numerologists, and trivia writers tie 1028 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 1028
Is 1028 a prime number?
1028 is composite with 6 total factors and the prime factorization 2^2 × 257.
What is the prime factorization of 1028?
It breaks down as 2^2 × 257, multiplying the primes 2 × 2 × 257.
How is 1028 represented in binary and hexadecimal?
1028 converts to 10000000100 in binary and 404 in hexadecimal, which are helpful for computer science applications.
Is 1028 a perfect square, cube, or triangular number?
1028 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1028?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.