3564
3564 is a even composite number that follows 3563 and precedes 3565. It is composed of 30 distinct factors: 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 81, 99, 108, 132, 162, 198, 297, 324, 396, 594, 891, 1188, 1782, 3564. Its prime factorization can be written as 2^2 × 3^4 × 11. 3564 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3564 is represented as 110111101100 in binary and DEC in hexadecimal. Historically, it is written as MMMDLXIV in Roman numerals.
Factor Analysis
30 FactorsProperties
The prime factorization (2^2 × 3^4 × 11) reveals 7 prime building blocks.
Divisible by 2
3564 ends in 4, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
3564 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 18 is a multiple of 9.
Divisible by 10
3564 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 3564 within several notable number theory sequences:
Timeline
Deep dive
How 3564 breaks down
3564 carries 30 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 6600, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110111101100 supports bitwise reasoning, hexadecimal DEC aligns with computing notation, and the Roman numeral MMMDLXIV keeps the encyclopedic tradition alive. These attributes make 3564 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3564 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3559–3569) to tune search ranges, and educators feature 3564 in worksheets about factor trees. Its binary footprint of length 12 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 3564 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 3564
Is 3564 a prime number?
3564 is composite with 30 total factors and the prime factorization 2^2 × 3^4 × 11.
What is the prime factorization of 3564?
It breaks down as 2^2 × 3^4 × 11, multiplying the primes 2 × 2 × 3 × 3 × 3 × 3 × 11.
How is 3564 represented in binary and hexadecimal?
3564 converts to 110111101100 in binary and DEC in hexadecimal, which are helpful for computer science applications.
Is 3564 a perfect square, cube, or triangular number?
3564 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3564?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.