309
309 is a odd composite number that follows 308 and precedes 310. It is composed of 4 distinct factors: 1, 3, 103, 309. Its prime factorization can be written as 3 × 103. 309 is classified as a deficient number based on the sum of its proper divisors. In computer science, 309 is represented as 100110101 in binary and 135 in hexadecimal. Historically, it is written as CCCIX in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (3 × 103) reveals 2 prime building blocks.
Divisible by 2
309 ends in 9, so it is odd.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 09 are not divisible by 4.
Divisible by 5
309 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 12 is not a multiple of 9.
Divisible by 10
309 does not end in 0.
Divisible by 11
The alternating digit sum 12 is not a multiple of 11.
Deficient classification and digit analytics place 309 within several notable number theory sequences:
Timeline
Deep dive
How 309 breaks down
309 carries 4 distinct factors and a digit signature of 12 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 107, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100110101 supports bitwise reasoning, hexadecimal 135 aligns with computing notation, and the Roman numeral CCCIX keeps the encyclopedic tradition alive. These attributes make 309 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 309 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (304–314) to tune search ranges, and educators feature 309 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 309 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 309
Is 309 a prime number?
309 is composite with 4 total factors and the prime factorization 3 × 103.
What is the prime factorization of 309?
It breaks down as 3 × 103, multiplying the primes 3 × 103.
How is 309 represented in binary and hexadecimal?
309 converts to 100110101 in binary and 135 in hexadecimal, which are helpful for computer science applications.
Is 309 a perfect square, cube, or triangular number?
309 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 309?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.