1564
1564 is a even composite number that follows 1563 and precedes 1565. It is composed of 12 distinct factors: 1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, 1564. Its prime factorization can be written as 2^2 × 17 × 23. 1564 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1564 is represented as 11000011100 in binary and 61C in hexadecimal. Historically, it is written as MDLXIV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 17 × 23) reveals 4 prime building blocks.
Divisible by 2
1564 ends in 4, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
1564 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 16 is not a multiple of 9.
Divisible by 10
1564 does not end in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Deficient classification and digit analytics place 1564 within several notable number theory sequences:
Timeline
Deep dive
How 1564 breaks down
1564 carries 12 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 1460, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11000011100 supports bitwise reasoning, hexadecimal 61C aligns with computing notation, and the Roman numeral MDLXIV keeps the encyclopedic tradition alive. These attributes make 1564 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1564 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1559–1569) to tune search ranges, and educators feature 1564 in worksheets about factor trees. Its binary footprint of length 11 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 1564 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 1564
Is 1564 a prime number?
1564 is composite with 12 total factors and the prime factorization 2^2 × 17 × 23.
What is the prime factorization of 1564?
It breaks down as 2^2 × 17 × 23, multiplying the primes 2 × 2 × 17 × 23.
How is 1564 represented in binary and hexadecimal?
1564 converts to 11000011100 in binary and 61C in hexadecimal, which are helpful for computer science applications.
Is 1564 a perfect square, cube, or triangular number?
1564 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1564?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.