8202
8202 is a even composite number that follows 8201 and precedes 8203. It is composed of 8 distinct factors: 1, 2, 3, 6, 1367, 2734, 4101, 8202. Its prime factorization can be written as 2 × 3 × 1367. 8202 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8202 is represented as 10000000001010 in binary and 200A in hexadecimal.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 1367) reveals 3 prime building blocks.
Divisible by 2
8202 ends in 2, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 02 are not divisible by 4.
Divisible by 5
8202 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 12 is not a multiple of 9.
Divisible by 10
8202 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 8202 within several notable number theory sequences:
Timeline
Deep dive
How 8202 breaks down
8202 carries 8 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 8214, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000000001010 supports bitwise reasoning, hexadecimal 200A aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8202 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8202 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8197–8207) to tune search ranges, and educators feature 8202 in worksheets about factor trees. Its binary footprint of length 14 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 8202 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 8202
Is 8202 a prime number?
8202 is composite with 8 total factors and the prime factorization 2 × 3 × 1367.
What is the prime factorization of 8202?
It breaks down as 2 × 3 × 1367, multiplying the primes 2 × 3 × 1367.
How is 8202 represented in binary and hexadecimal?
8202 converts to 10000000001010 in binary and 200A in hexadecimal, which are helpful for computer science applications.
Is 8202 a perfect square, cube, or triangular number?
8202 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8202?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.