1666
1666 is a even composite number that follows 1665 and precedes 1667. It is composed of 12 distinct factors: 1, 2, 7, 14, 17, 34, 49, 98, 119, 238, 833, 1666. Its prime factorization can be written as 2 × 7^2 × 17. 1666 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1666 is represented as 11010000010 in binary and 682 in hexadecimal. Historically, it is written as MDCLXVI in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 7^2 × 17) reveals 4 prime building blocks.
Divisible by 2
1666 ends in 6, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 66 are not divisible by 4.
Divisible by 5
1666 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 19 is not a multiple of 9.
Divisible by 10
1666 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Deficient classification and digit analytics place 1666 within several notable number theory sequences:
Timeline
Deep dive
How 1666 breaks down
1666 carries 12 distinct factors and a digit signature of 19 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 1412, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010000010 supports bitwise reasoning, hexadecimal 682 aligns with computing notation, and the Roman numeral MDCLXVI keeps the encyclopedic tradition alive. These attributes make 1666 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1666 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1661–1671) to tune search ranges, and educators feature 1666 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 1666 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 1666
Is 1666 a prime number?
1666 is composite with 12 total factors and the prime factorization 2 × 7^2 × 17.
What is the prime factorization of 1666?
It breaks down as 2 × 7^2 × 17, multiplying the primes 2 × 7 × 7 × 17.
How is 1666 represented in binary and hexadecimal?
1666 converts to 11010000010 in binary and 682 in hexadecimal, which are helpful for computer science applications.
Is 1666 a perfect square, cube, or triangular number?
1666 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1666?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.