3840
3840 is a even composite number that follows 3839 and precedes 3841. It is composed of 36 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 640, 768, 960, 1280, 1920, 3840. Its prime factorization can be written as 2^8 × 3 × 5. 3840 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3840 is represented as 111100000000 in binary and F00 in hexadecimal. Historically, it is written as MMMDCCCXL in Roman numerals.
Factor Analysis
36 FactorsProperties
The prime factorization (2^8 × 3 × 5) reveals 10 prime building blocks.
Divisible by 2
3840 ends in 0, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
3840 ends in 0, so it is divisible by 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 15 is not a multiple of 9.
Divisible by 10
3840 ends in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 3840 within several notable number theory sequences:
Timeline
Deep dive
How 3840 breaks down
3840 carries 36 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 8424, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111100000000 supports bitwise reasoning, hexadecimal F00 aligns with computing notation, and the Roman numeral MMMDCCCXL keeps the encyclopedic tradition alive. These attributes make 3840 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3840 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3835–3845) to tune search ranges, and educators feature 3840 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 3840 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 3840
Is 3840 a prime number?
3840 is composite with 36 total factors and the prime factorization 2^8 × 3 × 5.
What is the prime factorization of 3840?
It breaks down as 2^8 × 3 × 5, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5.
How is 3840 represented in binary and hexadecimal?
3840 converts to 111100000000 in binary and F00 in hexadecimal, which are helpful for computer science applications.
Is 3840 a perfect square, cube, or triangular number?
3840 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3840?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.