3192
3192 is a even composite number that follows 3191 and precedes 3193. It is composed of 32 distinct factors: 1, 2, 3, 4, 6, 7, 8, 12, 14, 19, 21, 24, 28, 38, 42, 56, 57, 76, 84, 114, 133, 152, 168, 228, 266, 399, 456, 532, 798, 1064, 1596, 3192. Its prime factorization can be written as 2^3 × 3 × 7 × 19. 3192 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3192 is represented as 110001111000 in binary and C78 in hexadecimal. Historically, it is written as MMMCXCII in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 3 × 7 × 19) reveals 6 prime building blocks.
Divisible by 2
3192 ends in 2, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 92 form a multiple of 4.
Divisible by 5
3192 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 15 is not a multiple of 9.
Divisible by 10
3192 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Abundant classification and digit analytics place 3192 within several notable number theory sequences:
Timeline
Deep dive
How 3192 breaks down
3192 carries 32 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 6408, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110001111000 supports bitwise reasoning, hexadecimal C78 aligns with computing notation, and the Roman numeral MMMCXCII keeps the encyclopedic tradition alive. These attributes make 3192 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3192 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3187–3197) to tune search ranges, and educators feature 3192 in worksheets about factor trees. Its binary footprint of length 12 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 3192 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 3192
Is 3192 a prime number?
3192 is composite with 32 total factors and the prime factorization 2^3 × 3 × 7 × 19.
What is the prime factorization of 3192?
It breaks down as 2^3 × 3 × 7 × 19, multiplying the primes 2 × 2 × 2 × 3 × 7 × 19.
How is 3192 represented in binary and hexadecimal?
3192 converts to 110001111000 in binary and C78 in hexadecimal, which are helpful for computer science applications.
Is 3192 a perfect square, cube, or triangular number?
3192 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3192?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.