803
803 is a odd composite number that follows 802 and precedes 804. It is composed of 4 distinct factors: 1, 11, 73, 803. Its prime factorization can be written as 11 × 73. 803 is classified as a deficient number based on the sum of its proper divisors. In computer science, 803 is represented as 1100100011 in binary and 323 in hexadecimal. Historically, it is written as DCCCIII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (11 × 73) reveals 2 prime building blocks.
Divisible by 2
803 ends in 3, so it is odd.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 03 are not divisible by 4.
Divisible by 5
803 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 11 is not a multiple of 9.
Divisible by 10
803 does not end in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Deficient classification and digit analytics place 803 within several notable number theory sequences:
Timeline
Deep dive
How 803 breaks down
803 carries 4 distinct factors and a digit signature of 11 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 85, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100100011 supports bitwise reasoning, hexadecimal 323 aligns with computing notation, and the Roman numeral DCCCIII keeps the encyclopedic tradition alive. These attributes make 803 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 803 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (798–808) to tune search ranges, and educators feature 803 in worksheets about factor trees. Its binary footprint of length 10 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 803 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 803
Is 803 a prime number?
803 is composite with 4 total factors and the prime factorization 11 × 73.
What is the prime factorization of 803?
It breaks down as 11 × 73, multiplying the primes 11 × 73.
How is 803 represented in binary and hexadecimal?
803 converts to 1100100011 in binary and 323 in hexadecimal, which are helpful for computer science applications.
Is 803 a perfect square, cube, or triangular number?
803 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 803?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.