312
312 is a even composite number that follows 311 and precedes 313. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. Its prime factorization can be written as 2^3 × 3 × 13. 312 is classified as a abundant number based on the sum of its proper divisors. In computer science, 312 is represented as 100111000 in binary and 138 in hexadecimal. Historically, it is written as CCCXII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 13) reveals 5 prime building blocks.
Divisible by 2
312 ends in 2, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 12 form a multiple of 4.
Divisible by 5
312 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 6 is not a multiple of 9.
Divisible by 10
312 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 312 within several notable number theory sequences:
Timeline
Deep dive
How 312 breaks down
312 carries 16 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 528, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100111000 supports bitwise reasoning, hexadecimal 138 aligns with computing notation, and the Roman numeral CCCXII keeps the encyclopedic tradition alive. These attributes make 312 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 312 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (307–317) to tune search ranges, and educators feature 312 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 312 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 312
Is 312 a prime number?
312 is composite with 16 total factors and the prime factorization 2^3 × 3 × 13.
What is the prime factorization of 312?
It breaks down as 2^3 × 3 × 13, multiplying the primes 2 × 2 × 2 × 3 × 13.
How is 312 represented in binary and hexadecimal?
312 converts to 100111000 in binary and 138 in hexadecimal, which are helpful for computer science applications.
Is 312 a perfect square, cube, or triangular number?
312 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 312?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.