802
802 is a even composite number that follows 801 and precedes 803. It is composed of 4 distinct factors: 1, 2, 401, 802. Its prime factorization can be written as 2 × 401. 802 is classified as a deficient number based on the sum of its proper divisors. In computer science, 802 is represented as 1100100010 in binary and 322 in hexadecimal. Historically, it is written as DCCCII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (2 × 401) reveals 2 prime building blocks.
Divisible by 2
802 ends in 2, so it is even.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 02 are not divisible by 4.
Divisible by 5
802 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 10 is not a multiple of 9.
Divisible by 10
802 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Deficient classification and digit analytics place 802 within several notable number theory sequences:
Timeline
Deep dive
How 802 breaks down
802 carries 4 distinct factors and a digit signature of 10 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 404, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100100010 supports bitwise reasoning, hexadecimal 322 aligns with computing notation, and the Roman numeral DCCCII keeps the encyclopedic tradition alive. These attributes make 802 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 802 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (797–807) to tune search ranges, and educators feature 802 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 802 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 802
Is 802 a prime number?
802 is composite with 4 total factors and the prime factorization 2 × 401.
What is the prime factorization of 802?
It breaks down as 2 × 401, multiplying the primes 2 × 401.
How is 802 represented in binary and hexadecimal?
802 converts to 1100100010 in binary and 322 in hexadecimal, which are helpful for computer science applications.
Is 802 a perfect square, cube, or triangular number?
802 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 802?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.