8464
8464 is a even composite number that follows 8463 and precedes 8465. It is composed of 15 distinct factors: 1, 2, 4, 8, 16, 23, 46, 92, 184, 368, 529, 1058, 2116, 4232, 8464. Its prime factorization can be written as 2^4 × 23^2. 8464 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8464 is represented as 10000100010000 in binary and 2110 in hexadecimal. It also belongs to the perfect square sequence.
Factor Analysis
15 FactorsProperties
The prime factorization (2^4 × 23^2) reveals 6 prime building blocks.
Divisible by 2
8464 ends in 4, so it is even.
Divisible by 3
The digit sum 22 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
8464 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 22 is not a multiple of 9.
Divisible by 10
8464 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 8464 within several notable number theory sequences:
Timeline
Deep dive
How 8464 breaks down
8464 carries 15 distinct factors and a digit signature of 22 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 8679, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000100010000 supports bitwise reasoning, hexadecimal 2110 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8464 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8464 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8459–8469) to tune search ranges, and educators feature 8464 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, Perfect squares) help historians, numerologists, and trivia writers tie 8464 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 8464
Is 8464 a prime number?
8464 is composite with 15 total factors and the prime factorization 2^4 × 23^2.
What is the prime factorization of 8464?
It breaks down as 2^4 × 23^2, multiplying the primes 2 × 2 × 2 × 2 × 23 × 23.
How is 8464 represented in binary and hexadecimal?
8464 converts to 10000100010000 in binary and 2110 in hexadecimal, which are helpful for computer science applications.
Is 8464 a perfect square, cube, or triangular number?
8464 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8464?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.