664
664 is a even composite number that follows 663 and precedes 665. It is composed of 8 distinct factors: 1, 2, 4, 8, 83, 166, 332, 664. Its prime factorization can be written as 2^3 × 83. 664 is classified as a deficient number based on the sum of its proper divisors. In computer science, 664 is represented as 1010011000 in binary and 298 in hexadecimal. Historically, it is written as DCLXIV in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2^3 × 83) reveals 4 prime building blocks.
Divisible by 2
664 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
664 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
664 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 664 within several notable number theory sequences:
Timeline
Deep dive
How 664 breaks down
664 carries 8 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 596, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010011000 supports bitwise reasoning, hexadecimal 298 aligns with computing notation, and the Roman numeral DCLXIV keeps the encyclopedic tradition alive. These attributes make 664 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 664 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (659–669) to tune search ranges, and educators feature 664 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, Deficient numbers) help historians, numerologists, and trivia writers tie 664 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 664
Is 664 a prime number?
664 is composite with 8 total factors and the prime factorization 2^3 × 83.
What is the prime factorization of 664?
It breaks down as 2^3 × 83, multiplying the primes 2 × 2 × 2 × 83.
How is 664 represented in binary and hexadecimal?
664 converts to 1010011000 in binary and 298 in hexadecimal, which are helpful for computer science applications.
Is 664 a perfect square, cube, or triangular number?
664 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 664?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.