8478
8478 is a even composite number that follows 8477 and precedes 8479. It is composed of 16 distinct factors: 1, 2, 3, 6, 9, 18, 27, 54, 157, 314, 471, 942, 1413, 2826, 4239, 8478. Its prime factorization can be written as 2 × 3^3 × 157. 8478 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8478 is represented as 10000100011110 in binary and 211E in hexadecimal.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3^3 × 157) reveals 5 prime building blocks.
Divisible by 2
8478 ends in 8, so it is even.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 78 are not divisible by 4.
Divisible by 5
8478 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 27 is a multiple of 9.
Divisible by 10
8478 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 8478 within several notable number theory sequences:
Timeline
Deep dive
How 8478 breaks down
8478 carries 16 distinct factors and a digit signature of 27 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 10482, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000100011110 supports bitwise reasoning, hexadecimal 211E aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8478 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8478 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8473–8483) to tune search ranges, and educators feature 8478 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 8478 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 8478
Is 8478 a prime number?
8478 is composite with 16 total factors and the prime factorization 2 × 3^3 × 157.
What is the prime factorization of 8478?
It breaks down as 2 × 3^3 × 157, multiplying the primes 2 × 3 × 3 × 3 × 157.
How is 8478 represented in binary and hexadecimal?
8478 converts to 10000100011110 in binary and 211E in hexadecimal, which are helpful for computer science applications.
Is 8478 a perfect square, cube, or triangular number?
8478 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8478?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.