801
801 is a odd composite number that follows 800 and precedes 802. It is composed of 6 distinct factors: 1, 3, 9, 89, 267, 801. Its prime factorization can be written as 3^2 × 89. 801 is classified as a deficient number based on the sum of its proper divisors. In computer science, 801 is represented as 1100100001 in binary and 321 in hexadecimal. Historically, it is written as DCCCI in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (3^2 × 89) reveals 3 prime building blocks.
Divisible by 2
801 ends in 1, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 01 are not divisible by 4.
Divisible by 5
801 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 9 is a multiple of 9.
Divisible by 10
801 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Deficient classification and digit analytics place 801 within several notable number theory sequences:
Timeline
Deep dive
How 801 breaks down
801 carries 6 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 369, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100100001 supports bitwise reasoning, hexadecimal 321 aligns with computing notation, and the Roman numeral DCCCI keeps the encyclopedic tradition alive. These attributes make 801 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 801 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (796–806) to tune search ranges, and educators feature 801 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 801 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 801
Is 801 a prime number?
801 is composite with 6 total factors and the prime factorization 3^2 × 89.
What is the prime factorization of 801?
It breaks down as 3^2 × 89, multiplying the primes 3 × 3 × 89.
How is 801 represented in binary and hexadecimal?
801 converts to 1100100001 in binary and 321 in hexadecimal, which are helpful for computer science applications.
Is 801 a perfect square, cube, or triangular number?
801 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 801?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.