396
396 is a even composite number that follows 395 and precedes 397. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396. Its prime factorization can be written as 2^2 × 3^2 × 11. 396 is classified as a abundant number based on the sum of its proper divisors. In computer science, 396 is represented as 110001100 in binary and 18C in hexadecimal. Historically, it is written as CCCXCVI in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 3^2 × 11) reveals 5 prime building blocks.
Divisible by 2
396 ends in 6, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 96 form a multiple of 4.
Divisible by 5
396 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
396 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 396 within several notable number theory sequences:
Timeline
Deep dive
How 396 breaks down
396 carries 18 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 696, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110001100 supports bitwise reasoning, hexadecimal 18C aligns with computing notation, and the Roman numeral CCCXCVI keeps the encyclopedic tradition alive. These attributes make 396 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 396 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (391–401) to tune search ranges, and educators feature 396 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 396 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 396
Is 396 a prime number?
396 is composite with 18 total factors and the prime factorization 2^2 × 3^2 × 11.
What is the prime factorization of 396?
It breaks down as 2^2 × 3^2 × 11, multiplying the primes 2 × 2 × 3 × 3 × 11.
How is 396 represented in binary and hexadecimal?
396 converts to 110001100 in binary and 18C in hexadecimal, which are helpful for computer science applications.
Is 396 a perfect square, cube, or triangular number?
396 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 396?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.