228
228 is a even composite number that follows 227 and precedes 229. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228. Its prime factorization can be written as 2^2 × 3 × 19. 228 is classified as a abundant number based on the sum of its proper divisors. In computer science, 228 is represented as 11100100 in binary and E4 in hexadecimal. Historically, it is written as CCXXVIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3 × 19) reveals 4 prime building blocks.
Divisible by 2
228 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
228 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
228 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 228 within several notable number theory sequences:
Timeline
Deep dive
How 228 breaks down
228 carries 12 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 332, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100100 supports bitwise reasoning, hexadecimal E4 aligns with computing notation, and the Roman numeral CCXXVIII keeps the encyclopedic tradition alive. These attributes make 228 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 228 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (223–233) to tune search ranges, and educators feature 228 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, Abundant numbers) help historians, numerologists, and trivia writers tie 228 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 228
Is 228 a prime number?
228 is composite with 12 total factors and the prime factorization 2^2 × 3 × 19.
What is the prime factorization of 228?
It breaks down as 2^2 × 3 × 19, multiplying the primes 2 × 2 × 3 × 19.
How is 228 represented in binary and hexadecimal?
228 converts to 11100100 in binary and E4 in hexadecimal, which are helpful for computer science applications.
Is 228 a perfect square, cube, or triangular number?
228 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 228?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.