666
666 is a even composite number that follows 665 and precedes 667. It is composed of 12 distinct factors: 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666. Its prime factorization can be written as 2 × 3^2 × 37. 666 is classified as a abundant number based on the sum of its proper divisors. In computer science, 666 is represented as 1010011010 in binary and 29A in hexadecimal. Historically, it is written as DCLXVI in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3^2 × 37) reveals 4 prime building blocks.
Divisible by 2
666 ends in 6, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 66 are not divisible by 4.
Divisible by 5
666 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
666 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 666 within several notable number theory sequences:
Timeline
Deep dive
How 666 breaks down
666 carries 12 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 816, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010011010 supports bitwise reasoning, hexadecimal 29A aligns with computing notation, and the Roman numeral DCLXVI keeps the encyclopedic tradition alive. These attributes make 666 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 666 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (661–671) to tune search ranges, and educators feature 666 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, Triangular numbers) help historians, numerologists, and trivia writers tie 666 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 666
Is 666 a prime number?
666 is composite with 12 total factors and the prime factorization 2 × 3^2 × 37.
What is the prime factorization of 666?
It breaks down as 2 × 3^2 × 37, multiplying the primes 2 × 3 × 3 × 37.
How is 666 represented in binary and hexadecimal?
666 converts to 1010011010 in binary and 29A in hexadecimal, which are helpful for computer science applications.
Is 666 a perfect square, cube, or triangular number?
666 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 666?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.