1664
1664 is a even composite number that follows 1663 and precedes 1665. It is composed of 16 distinct factors: 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664. Its prime factorization can be written as 2^7 × 13. 1664 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1664 is represented as 11010000000 in binary and 680 in hexadecimal. Historically, it is written as MDCLXIV in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^7 × 13) reveals 8 prime building blocks.
Divisible by 2
1664 ends in 4, so it is even.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
1664 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 17 is not a multiple of 9.
Divisible by 10
1664 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 1664 within several notable number theory sequences:
Timeline
Deep dive
How 1664 breaks down
1664 carries 16 distinct factors and a digit signature of 17 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 1906, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010000000 supports bitwise reasoning, hexadecimal 680 aligns with computing notation, and the Roman numeral MDCLXIV keeps the encyclopedic tradition alive. These attributes make 1664 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1664 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1659–1669) to tune search ranges, and educators feature 1664 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, Abundant numbers) help historians, numerologists, and trivia writers tie 1664 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 1664
Is 1664 a prime number?
1664 is composite with 16 total factors and the prime factorization 2^7 × 13.
What is the prime factorization of 1664?
It breaks down as 2^7 × 13, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 13.
How is 1664 represented in binary and hexadecimal?
1664 converts to 11010000000 in binary and 680 in hexadecimal, which are helpful for computer science applications.
Is 1664 a perfect square, cube, or triangular number?
1664 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1664?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.