4864
4864 is a even composite number that follows 4863 and precedes 4865. It is composed of 18 distinct factors: 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 608, 1216, 2432, 4864. Its prime factorization can be written as 2^8 × 19. 4864 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4864 is represented as 1001100000000 in binary and 1300 in hexadecimal.
Factor Analysis
18 FactorsProperties
The prime factorization (2^8 × 19) reveals 9 prime building blocks.
Divisible by 2
4864 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
4864 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
4864 does not end in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 4864 within several notable number theory sequences:
Timeline
Deep dive
How 4864 breaks down
4864 carries 18 distinct factors and a digit signature of 22 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 5356, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001100000000 supports bitwise reasoning, hexadecimal 1300 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4864 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4864 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4859–4869) to tune search ranges, and educators feature 4864 in worksheets about factor trees. Its binary footprint of length 13 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 4864 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 4864
Is 4864 a prime number?
4864 is composite with 18 total factors and the prime factorization 2^8 × 19.
What is the prime factorization of 4864?
It breaks down as 2^8 × 19, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 19.
How is 4864 represented in binary and hexadecimal?
4864 converts to 1001100000000 in binary and 1300 in hexadecimal, which are helpful for computer science applications.
Is 4864 a perfect square, cube, or triangular number?
4864 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4864?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.