192
192 is a even composite number that follows 191 and precedes 193. It is composed of 14 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. Its prime factorization can be written as 2^6 × 3. 192 is classified as a abundant number based on the sum of its proper divisors. In computer science, 192 is represented as 11000000 in binary and C0 in hexadecimal. Historically, it is written as CXCII in Roman numerals.
Factor Analysis
14 FactorsProperties
The prime factorization (2^6 × 3) reveals 7 prime building blocks.
Divisible by 2
192 ends in 2, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 92 form a multiple of 4.
Divisible by 5
192 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
192 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 192 within several notable number theory sequences:
Timeline
Deep dive
How 192 breaks down
192 carries 14 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 316, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11000000 supports bitwise reasoning, hexadecimal C0 aligns with computing notation, and the Roman numeral CXCII keeps the encyclopedic tradition alive. These attributes make 192 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 192 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (187–197) to tune search ranges, and educators feature 192 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 192 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 192
Is 192 a prime number?
192 is composite with 14 total factors and the prime factorization 2^6 × 3.
What is the prime factorization of 192?
It breaks down as 2^6 × 3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 3.
How is 192 represented in binary and hexadecimal?
192 converts to 11000000 in binary and C0 in hexadecimal, which are helpful for computer science applications.
Is 192 a perfect square, cube, or triangular number?
192 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 192?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.