321
321 is a odd composite number that follows 320 and precedes 322. It is composed of 4 distinct factors: 1, 3, 107, 321. Its prime factorization can be written as 3 × 107. 321 is classified as a deficient number based on the sum of its proper divisors. In computer science, 321 is represented as 101000001 in binary and 141 in hexadecimal. Historically, it is written as CCCXXI in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (3 × 107) reveals 2 prime building blocks.
Divisible by 2
321 ends in 1, so it is odd.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 21 are not divisible by 4.
Divisible by 5
321 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 6 is not a multiple of 9.
Divisible by 10
321 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Deficient classification and digit analytics place 321 within several notable number theory sequences:
Timeline
Deep dive
How 321 breaks down
321 carries 4 distinct factors and a digit signature of 6 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 111, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101000001 supports bitwise reasoning, hexadecimal 141 aligns with computing notation, and the Roman numeral CCCXXI keeps the encyclopedic tradition alive. These attributes make 321 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 321 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (316–326) to tune search ranges, and educators feature 321 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, Deficient numbers) help historians, numerologists, and trivia writers tie 321 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 321
Is 321 a prime number?
321 is composite with 4 total factors and the prime factorization 3 × 107.
What is the prime factorization of 321?
It breaks down as 3 × 107, multiplying the primes 3 × 107.
How is 321 represented in binary and hexadecimal?
321 converts to 101000001 in binary and 141 in hexadecimal, which are helpful for computer science applications.
Is 321 a perfect square, cube, or triangular number?
321 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 321?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.