1128
1128 is a even composite number that follows 1127 and precedes 1129. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 24, 47, 94, 141, 188, 282, 376, 564, 1128. Its prime factorization can be written as 2^3 × 3 × 47. 1128 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1128 is represented as 10001101000 in binary and 468 in hexadecimal. Historically, it is written as MCXXVIII in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 47) reveals 5 prime building blocks.
Divisible by 2
1128 ends in 8, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
1128 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
1128 does not end in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Abundant classification and digit analytics place 1128 within several notable number theory sequences:
Timeline
Deep dive
How 1128 breaks down
1128 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 1752, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10001101000 supports bitwise reasoning, hexadecimal 468 aligns with computing notation, and the Roman numeral MCXXVIII keeps the encyclopedic tradition alive. These attributes make 1128 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1128 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1123–1133) to tune search ranges, and educators feature 1128 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, Triangular numbers) help historians, numerologists, and trivia writers tie 1128 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 1128
Is 1128 a prime number?
1128 is composite with 16 total factors and the prime factorization 2^3 × 3 × 47.
What is the prime factorization of 1128?
It breaks down as 2^3 × 3 × 47, multiplying the primes 2 × 2 × 2 × 3 × 47.
How is 1128 represented in binary and hexadecimal?
1128 converts to 10001101000 in binary and 468 in hexadecimal, which are helpful for computer science applications.
Is 1128 a perfect square, cube, or triangular number?
1128 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 1128?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.