648
648 is a even composite number that follows 647 and precedes 649. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648. Its prime factorization can be written as 2^3 × 3^4. 648 is classified as a abundant number based on the sum of its proper divisors. In computer science, 648 is represented as 1010001000 in binary and 288 in hexadecimal. Historically, it is written as DCXLVIII in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^3 × 3^4) reveals 7 prime building blocks.
Divisible by 2
648 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
648 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
648 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Abundant classification and digit analytics place 648 within several notable number theory sequences:
Timeline
Deep dive
How 648 breaks down
648 carries 20 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1167, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010001000 supports bitwise reasoning, hexadecimal 288 aligns with computing notation, and the Roman numeral DCXLVIII keeps the encyclopedic tradition alive. These attributes make 648 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 648 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (643–653) to tune search ranges, and educators feature 648 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) help historians, numerologists, and trivia writers tie 648 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 648
Is 648 a prime number?
648 is composite with 20 total factors and the prime factorization 2^3 × 3^4.
What is the prime factorization of 648?
It breaks down as 2^3 × 3^4, multiplying the primes 2 × 2 × 2 × 3 × 3 × 3 × 3.
How is 648 represented in binary and hexadecimal?
648 converts to 1010001000 in binary and 288 in hexadecimal, which are helpful for computer science applications.
Is 648 a perfect square, cube, or triangular number?
648 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 648?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.