1649
1649 is a odd composite number that follows 1648 and precedes 1650. It is composed of 4 distinct factors: 1, 17, 97, 1649. Its prime factorization can be written as 17 × 97. 1649 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1649 is represented as 11001110001 in binary and 671 in hexadecimal. Historically, it is written as MDCXLIX in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (17 × 97) reveals 2 prime building blocks.
Divisible by 2
1649 ends in 9, so it is odd.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 49 are not divisible by 4.
Divisible by 5
1649 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 20 is not a multiple of 9.
Divisible by 10
1649 does not end in 0.
Divisible by 11
The alternating digit sum -10 is not a multiple of 11.
Deficient classification and digit analytics place 1649 within several notable number theory sequences:
Timeline
Deep dive
How 1649 breaks down
1649 carries 4 distinct factors and a digit signature of 20 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 115, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11001110001 supports bitwise reasoning, hexadecimal 671 aligns with computing notation, and the Roman numeral MDCXLIX keeps the encyclopedic tradition alive. These attributes make 1649 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1649 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1644–1654) to tune search ranges, and educators feature 1649 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 1649 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 1649
Is 1649 a prime number?
1649 is composite with 4 total factors and the prime factorization 17 × 97.
What is the prime factorization of 1649?
It breaks down as 17 × 97, multiplying the primes 17 × 97.
How is 1649 represented in binary and hexadecimal?
1649 converts to 11001110001 in binary and 671 in hexadecimal, which are helpful for computer science applications.
Is 1649 a perfect square, cube, or triangular number?
1649 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1649?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.