3792
3792 is a even composite number that follows 3791 and precedes 3793. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 79, 158, 237, 316, 474, 632, 948, 1264, 1896, 3792. Its prime factorization can be written as 2^4 × 3 × 79. 3792 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3792 is represented as 111011010000 in binary and ED0 in hexadecimal. Historically, it is written as MMMDCCXCII in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 79) reveals 6 prime building blocks.
Divisible by 2
3792 ends in 2, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 92 form a multiple of 4.
Divisible by 5
3792 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 21 is not a multiple of 9.
Divisible by 10
3792 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 3792 within several notable number theory sequences:
Timeline
Deep dive
How 3792 breaks down
3792 carries 20 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 6128, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111011010000 supports bitwise reasoning, hexadecimal ED0 aligns with computing notation, and the Roman numeral MMMDCCXCII keeps the encyclopedic tradition alive. These attributes make 3792 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3792 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3787–3797) to tune search ranges, and educators feature 3792 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 3792 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 3792
Is 3792 a prime number?
3792 is composite with 20 total factors and the prime factorization 2^4 × 3 × 79.
What is the prime factorization of 3792?
It breaks down as 2^4 × 3 × 79, multiplying the primes 2 × 2 × 2 × 2 × 3 × 79.
How is 3792 represented in binary and hexadecimal?
3792 converts to 111011010000 in binary and ED0 in hexadecimal, which are helpful for computer science applications.
Is 3792 a perfect square, cube, or triangular number?
3792 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3792?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.