7564
7564 is a even composite number that follows 7563 and precedes 7565. It is composed of 12 distinct factors: 1, 2, 4, 31, 61, 62, 122, 124, 244, 1891, 3782, 7564. Its prime factorization can be written as 2^2 × 31 × 61. 7564 is classified as a deficient number based on the sum of its proper divisors. In computer science, 7564 is represented as 1110110001100 in binary and 1D8C in hexadecimal.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 31 × 61) reveals 4 prime building blocks.
Divisible by 2
7564 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
7564 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
7564 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Deficient classification and digit analytics place 7564 within several notable number theory sequences:
Timeline
Deep dive
How 7564 breaks down
7564 carries 12 distinct factors and a digit signature of 22 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 6324, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1110110001100 supports bitwise reasoning, hexadecimal 1D8C aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7564 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7564 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7559–7569) to tune search ranges, and educators feature 7564 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, Deficient numbers) help historians, numerologists, and trivia writers tie 7564 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 7564
Is 7564 a prime number?
7564 is composite with 12 total factors and the prime factorization 2^2 × 31 × 61.
What is the prime factorization of 7564?
It breaks down as 2^2 × 31 × 61, multiplying the primes 2 × 2 × 31 × 61.
How is 7564 represented in binary and hexadecimal?
7564 converts to 1110110001100 in binary and 1D8C in hexadecimal, which are helpful for computer science applications.
Is 7564 a perfect square, cube, or triangular number?
7564 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7564?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.