3006
3006 is a even composite number that follows 3005 and precedes 3007. It is composed of 12 distinct factors: 1, 2, 3, 6, 9, 18, 167, 334, 501, 1002, 1503, 3006. Its prime factorization can be written as 2 × 3^2 × 167. 3006 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3006 is represented as 101110111110 in binary and BBE in hexadecimal. Historically, it is written as MMMVI in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3^2 × 167) reveals 4 prime building blocks.
Divisible by 2
3006 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
3006 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
3006 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 3006 within several notable number theory sequences:
Timeline
Deep dive
How 3006 breaks down
3006 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 3546, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101110111110 supports bitwise reasoning, hexadecimal BBE aligns with computing notation, and the Roman numeral MMMVI keeps the encyclopedic tradition alive. These attributes make 3006 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3006 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3001–3011) to tune search ranges, and educators feature 3006 in worksheets about factor trees. Its binary footprint of length 12 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 3006 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 3006
Is 3006 a prime number?
3006 is composite with 12 total factors and the prime factorization 2 × 3^2 × 167.
What is the prime factorization of 3006?
It breaks down as 2 × 3^2 × 167, multiplying the primes 2 × 3 × 3 × 167.
How is 3006 represented in binary and hexadecimal?
3006 converts to 101110111110 in binary and BBE in hexadecimal, which are helpful for computer science applications.
Is 3006 a perfect square, cube, or triangular number?
3006 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3006?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.