128
128 is a even composite number that follows 127 and precedes 129. It is composed of 8 distinct factors: 1, 2, 4, 8, 16, 32, 64, 128. Its prime factorization can be written as 2^7. 128 is classified as a deficient number based on the sum of its proper divisors. In computer science, 128 is represented as 10000000 in binary and 80 in hexadecimal. Historically, it is written as CXXVIII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2^7) reveals 7 prime building blocks.
Divisible by 2
128 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
128 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
128 does not end in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Deficient classification and digit analytics place 128 within several notable number theory sequences:
Timeline
Deep dive
How 128 breaks down
128 carries 8 distinct factors and a digit signature of 11 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 127, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000000 supports bitwise reasoning, hexadecimal 80 aligns with computing notation, and the Roman numeral CXXVIII keeps the encyclopedic tradition alive. These attributes make 128 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 128 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (123–133) to tune search ranges, and educators feature 128 in worksheets about factor trees. Its binary footprint of length 8 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 128 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 128
Is 128 a prime number?
128 is composite with 8 total factors and the prime factorization 2^7.
What is the prime factorization of 128?
It breaks down as 2^7, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2.
How is 128 represented in binary and hexadecimal?
128 converts to 10000000 in binary and 80 in hexadecimal, which are helpful for computer science applications.
Is 128 a perfect square, cube, or triangular number?
128 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 128?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.