392
392 is a even composite number that follows 391 and precedes 393. It is composed of 12 distinct factors: 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392. Its prime factorization can be written as 2^3 × 7^2. 392 is classified as a abundant number based on the sum of its proper divisors. In computer science, 392 is represented as 110001000 in binary and 188 in hexadecimal. Historically, it is written as CCCXCII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^3 × 7^2) reveals 5 prime building blocks.
Divisible by 2
392 ends in 2, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 92 form a multiple of 4.
Divisible by 5
392 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 14 is not a multiple of 9.
Divisible by 10
392 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 392 within several notable number theory sequences:
Timeline
Deep dive
How 392 breaks down
392 carries 12 distinct factors and a digit signature of 14 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 463, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110001000 supports bitwise reasoning, hexadecimal 188 aligns with computing notation, and the Roman numeral CCCXCII keeps the encyclopedic tradition alive. These attributes make 392 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 392 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (387–397) to tune search ranges, and educators feature 392 in worksheets about factor trees. Its binary footprint of length 9 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 392 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 392
Is 392 a prime number?
392 is composite with 12 total factors and the prime factorization 2^3 × 7^2.
What is the prime factorization of 392?
It breaks down as 2^3 × 7^2, multiplying the primes 2 × 2 × 2 × 7 × 7.
How is 392 represented in binary and hexadecimal?
392 converts to 110001000 in binary and 188 in hexadecimal, which are helpful for computer science applications.
Is 392 a perfect square, cube, or triangular number?
392 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 392?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.