3003
3003 is a odd composite number that follows 3002 and precedes 3004. It is composed of 16 distinct factors: 1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003. Its prime factorization can be written as 3 × 7 × 11 × 13. 3003 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3003 is represented as 101110111011 in binary and BBB in hexadecimal. Historically, it is written as MMMIII in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
16 FactorsProperties
The prime factorization (3 × 7 × 11 × 13) reveals 4 prime building blocks.
Divisible by 2
3003 ends in 3, so it is odd.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 03 are not divisible by 4.
Divisible by 5
3003 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
3003 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 3003 within several notable number theory sequences:
Timeline
Deep dive
How 3003 breaks down
3003 carries 16 distinct factors and a digit signature of 6 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 2373, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101110111011 supports bitwise reasoning, hexadecimal BBB aligns with computing notation, and the Roman numeral MMMIII keeps the encyclopedic tradition alive. These attributes make 3003 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3003 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2998–3008) to tune search ranges, and educators feature 3003 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, Deficient numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 3003 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 3003
Is 3003 a prime number?
3003 is composite with 16 total factors and the prime factorization 3 × 7 × 11 × 13.
What is the prime factorization of 3003?
It breaks down as 3 × 7 × 11 × 13, multiplying the primes 3 × 7 × 11 × 13.
How is 3003 represented in binary and hexadecimal?
3003 converts to 101110111011 in binary and BBB in hexadecimal, which are helpful for computer science applications.
Is 3003 a perfect square, cube, or triangular number?
3003 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 3003?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.