800
800 is a even composite number that follows 799 and precedes 801. It is composed of 18 distinct factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800. Its prime factorization can be written as 2^5 × 5^2. 800 is classified as a abundant number based on the sum of its proper divisors. In computer science, 800 is represented as 1100100000 in binary and 320 in hexadecimal. Historically, it is written as DCCC in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^5 × 5^2) reveals 7 prime building blocks.
Divisible by 2
800 ends in 0, so it is even.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
800 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 8 is not a multiple of 9.
Divisible by 10
800 ends in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 800 within several notable number theory sequences:
Timeline
Deep dive
How 800 breaks down
800 carries 18 distinct factors and a digit signature of 8 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 1153, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100100000 supports bitwise reasoning, hexadecimal 320 aligns with computing notation, and the Roman numeral DCCC keeps the encyclopedic tradition alive. These attributes make 800 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 800 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (795–805) to tune search ranges, and educators feature 800 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, Abundant numbers) help historians, numerologists, and trivia writers tie 800 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 800
Is 800 a prime number?
800 is composite with 18 total factors and the prime factorization 2^5 × 5^2.
What is the prime factorization of 800?
It breaks down as 2^5 × 5^2, multiplying the primes 2 × 2 × 2 × 2 × 2 × 5 × 5.
How is 800 represented in binary and hexadecimal?
800 converts to 1100100000 in binary and 320 in hexadecimal, which are helpful for computer science applications.
Is 800 a perfect square, cube, or triangular number?
800 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 800?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.