807
807 is a odd composite number that follows 806 and precedes 808. It is composed of 4 distinct factors: 1, 3, 269, 807. Its prime factorization can be written as 3 × 269. 807 is classified as a deficient number based on the sum of its proper divisors. In computer science, 807 is represented as 1100100111 in binary and 327 in hexadecimal. Historically, it is written as DCCCVII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (3 × 269) reveals 2 prime building blocks.
Divisible by 2
807 ends in 7, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 07 are not divisible by 4.
Divisible by 5
807 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 15 is not a multiple of 9.
Divisible by 10
807 does not end in 0.
Divisible by 11
The alternating digit sum 15 is not a multiple of 11.
Deficient classification and digit analytics place 807 within several notable number theory sequences:
Timeline
Deep dive
How 807 breaks down
807 carries 4 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 273, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100100111 supports bitwise reasoning, hexadecimal 327 aligns with computing notation, and the Roman numeral DCCCVII keeps the encyclopedic tradition alive. These attributes make 807 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 807 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (802–812) to tune search ranges, and educators feature 807 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 807 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 807
Is 807 a prime number?
807 is composite with 4 total factors and the prime factorization 3 × 269.
What is the prime factorization of 807?
It breaks down as 3 × 269, multiplying the primes 3 × 269.
How is 807 represented in binary and hexadecimal?
807 converts to 1100100111 in binary and 327 in hexadecimal, which are helpful for computer science applications.
Is 807 a perfect square, cube, or triangular number?
807 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 807?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.