306
306 is a even composite number that follows 305 and precedes 307. It is composed of 12 distinct factors: 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. Its prime factorization can be written as 2 × 3^2 × 17. 306 is classified as a abundant number based on the sum of its proper divisors. In computer science, 306 is represented as 100110010 in binary and 132 in hexadecimal. Historically, it is written as CCCVI in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3^2 × 17) reveals 4 prime building blocks.
Divisible by 2
306 ends in 6, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 06 are not divisible by 4.
Divisible by 5
306 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 9 is a multiple of 9.
Divisible by 10
306 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Abundant classification and digit analytics place 306 within several notable number theory sequences:
Timeline
Deep dive
How 306 breaks down
306 carries 12 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 396, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100110010 supports bitwise reasoning, hexadecimal 132 aligns with computing notation, and the Roman numeral CCCVI keeps the encyclopedic tradition alive. These attributes make 306 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 306 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (301–311) to tune search ranges, and educators feature 306 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 306 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 306
Is 306 a prime number?
306 is composite with 12 total factors and the prime factorization 2 × 3^2 × 17.
What is the prime factorization of 306?
It breaks down as 2 × 3^2 × 17, multiplying the primes 2 × 3 × 3 × 17.
How is 306 represented in binary and hexadecimal?
306 converts to 100110010 in binary and 132 in hexadecimal, which are helpful for computer science applications.
Is 306 a perfect square, cube, or triangular number?
306 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 306?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.