8214
8214 is a even composite number that follows 8213 and precedes 8215. It is composed of 12 distinct factors: 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214. Its prime factorization can be written as 2 × 3 × 37^2. 8214 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8214 is represented as 10000000010110 in binary and 2016 in hexadecimal.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3 × 37^2) reveals 4 prime building blocks.
Divisible by 2
8214 ends in 4, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 14 are not divisible by 4.
Divisible by 5
8214 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 15 is not a multiple of 9.
Divisible by 10
8214 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 8214 within several notable number theory sequences:
Timeline
Deep dive
How 8214 breaks down
8214 carries 12 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 8670, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000000010110 supports bitwise reasoning, hexadecimal 2016 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8214 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8214 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8209–8219) to tune search ranges, and educators feature 8214 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 8214 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 8214
Is 8214 a prime number?
8214 is composite with 12 total factors and the prime factorization 2 × 3 × 37^2.
What is the prime factorization of 8214?
It breaks down as 2 × 3 × 37^2, multiplying the primes 2 × 3 × 37 × 37.
How is 8214 represented in binary and hexadecimal?
8214 converts to 10000000010110 in binary and 2016 in hexadecimal, which are helpful for computer science applications.
Is 8214 a perfect square, cube, or triangular number?
8214 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8214?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.