792
792 is a even composite number that follows 791 and precedes 793. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 132, 198, 264, 396, 792. Its prime factorization can be written as 2^3 × 3^2 × 11. 792 is classified as a abundant number based on the sum of its proper divisors. In computer science, 792 is represented as 1100011000 in binary and 318 in hexadecimal. Historically, it is written as DCCXCII in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^3 × 3^2 × 11) reveals 6 prime building blocks.
Divisible by 2
792 ends in 2, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 92 form a multiple of 4.
Divisible by 5
792 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
792 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 792 within several notable number theory sequences:
Timeline
Deep dive
How 792 breaks down
792 carries 24 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1548, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100011000 supports bitwise reasoning, hexadecimal 318 aligns with computing notation, and the Roman numeral DCCXCII keeps the encyclopedic tradition alive. These attributes make 792 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 792 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (787–797) to tune search ranges, and educators feature 792 in worksheets about factor trees. Its binary footprint of length 10 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 792 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 792
Is 792 a prime number?
792 is composite with 24 total factors and the prime factorization 2^3 × 3^2 × 11.
What is the prime factorization of 792?
It breaks down as 2^3 × 3^2 × 11, multiplying the primes 2 × 2 × 2 × 3 × 3 × 11.
How is 792 represented in binary and hexadecimal?
792 converts to 1100011000 in binary and 318 in hexadecimal, which are helpful for computer science applications.
Is 792 a perfect square, cube, or triangular number?
792 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 792?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.