3648
3648 is a even composite number that follows 3647 and precedes 3649. It is composed of 28 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 152, 192, 228, 304, 456, 608, 912, 1216, 1824, 3648. Its prime factorization can be written as 2^6 × 3 × 19. 3648 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3648 is represented as 111001000000 in binary and E40 in hexadecimal. Historically, it is written as MMMDCXLVIII in Roman numerals.
Factor Analysis
28 FactorsProperties
The prime factorization (2^6 × 3 × 19) reveals 8 prime building blocks.
Divisible by 2
3648 ends in 8, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
3648 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 21 is not a multiple of 9.
Divisible by 10
3648 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Abundant classification and digit analytics place 3648 within several notable number theory sequences:
Timeline
Deep dive
How 3648 breaks down
3648 carries 28 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 6512, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111001000000 supports bitwise reasoning, hexadecimal E40 aligns with computing notation, and the Roman numeral MMMDCXLVIII keeps the encyclopedic tradition alive. These attributes make 3648 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3648 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3643–3653) to tune search ranges, and educators feature 3648 in worksheets about factor trees. Its binary footprint of length 12 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 3648 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 3648
Is 3648 a prime number?
3648 is composite with 28 total factors and the prime factorization 2^6 × 3 × 19.
What is the prime factorization of 3648?
It breaks down as 2^6 × 3 × 19, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 3 × 19.
How is 3648 represented in binary and hexadecimal?
3648 converts to 111001000000 in binary and E40 in hexadecimal, which are helpful for computer science applications.
Is 3648 a perfect square, cube, or triangular number?
3648 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3648?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.