564
564 is a even composite number that follows 563 and precedes 565. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564. Its prime factorization can be written as 2^2 × 3 × 47. 564 is classified as a abundant number based on the sum of its proper divisors. In computer science, 564 is represented as 1000110100 in binary and 234 in hexadecimal. Historically, it is written as DLXIV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3 × 47) reveals 4 prime building blocks.
Divisible by 2
564 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 64 form a multiple of 4.
Divisible by 5
564 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
564 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 564 within several notable number theory sequences:
Timeline
Deep dive
How 564 breaks down
564 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 780, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000110100 supports bitwise reasoning, hexadecimal 234 aligns with computing notation, and the Roman numeral DLXIV keeps the encyclopedic tradition alive. These attributes make 564 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 564 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (559–569) to tune search ranges, and educators feature 564 in worksheets about factor trees. Its binary footprint of length 10 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 564 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 564
Is 564 a prime number?
564 is composite with 12 total factors and the prime factorization 2^2 × 3 × 47.
What is the prime factorization of 564?
It breaks down as 2^2 × 3 × 47, multiplying the primes 2 × 2 × 3 × 47.
How is 564 represented in binary and hexadecimal?
564 converts to 1000110100 in binary and 234 in hexadecimal, which are helpful for computer science applications.
Is 564 a perfect square, cube, or triangular number?
564 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 564?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.