198
198 is a even composite number that follows 197 and precedes 199. It is composed of 12 distinct factors: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198. Its prime factorization can be written as 2 × 3^2 × 11. 198 is classified as a abundant number based on the sum of its proper divisors. In computer science, 198 is represented as 11000110 in binary and C6 in hexadecimal. Historically, it is written as CXCVIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3^2 × 11) reveals 4 prime building blocks.
Divisible by 2
198 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 98 are not divisible by 4.
Divisible by 5
198 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 18 is a multiple of 9.
Divisible by 10
198 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 198 within several notable number theory sequences:
Timeline
Deep dive
How 198 breaks down
198 carries 12 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 270, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11000110 supports bitwise reasoning, hexadecimal C6 aligns with computing notation, and the Roman numeral CXCVIII keeps the encyclopedic tradition alive. These attributes make 198 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 198 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (193–203) to tune search ranges, and educators feature 198 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 198 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 198
Is 198 a prime number?
198 is composite with 12 total factors and the prime factorization 2 × 3^2 × 11.
What is the prime factorization of 198?
It breaks down as 2 × 3^2 × 11, multiplying the primes 2 × 3 × 3 × 11.
How is 198 represented in binary and hexadecimal?
198 converts to 11000110 in binary and C6 in hexadecimal, which are helpful for computer science applications.
Is 198 a perfect square, cube, or triangular number?
198 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 198?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.