1648
1648 is a even composite number that follows 1647 and precedes 1649. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 103, 206, 412, 824, 1648. Its prime factorization can be written as 2^4 × 103. 1648 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1648 is represented as 11001110000 in binary and 670 in hexadecimal. Historically, it is written as MDCXLVIII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 103) reveals 5 prime building blocks.
Divisible by 2
1648 ends in 8, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
1648 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
1648 does not end in 0.
Divisible by 11
The alternating digit sum -9 is not a multiple of 11.
Deficient classification and digit analytics place 1648 within several notable number theory sequences:
Timeline
Deep dive
How 1648 breaks down
1648 carries 10 distinct factors and a digit signature of 19 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 1576, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11001110000 supports bitwise reasoning, hexadecimal 670 aligns with computing notation, and the Roman numeral MDCXLVIII keeps the encyclopedic tradition alive. These attributes make 1648 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1648 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1643–1653) to tune search ranges, and educators feature 1648 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 1648 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 1648
Is 1648 a prime number?
1648 is composite with 10 total factors and the prime factorization 2^4 × 103.
What is the prime factorization of 1648?
It breaks down as 2^4 × 103, multiplying the primes 2 × 2 × 2 × 2 × 103.
How is 1648 represented in binary and hexadecimal?
1648 converts to 11001110000 in binary and 670 in hexadecimal, which are helpful for computer science applications.
Is 1648 a perfect square, cube, or triangular number?
1648 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1648?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.