6840
6840 is a even composite number that follows 6839 and precedes 6841. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 30, 36, 38, 40, 45, 57, 60, 72, 76, 90, 95, 114, 120, 152, 171, 180, 190, 228, 285, 342, 360, 380, 456, 570, 684, 760, 855, 1140, 1368, 1710, 2280, 3420, 6840. Its prime factorization can be written as 2^3 × 3^2 × 5 × 19. 6840 is classified as a abundant number based on the sum of its proper divisors. In computer science, 6840 is represented as 1101010111000 in binary and 1AB8 in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^3 × 3^2 × 5 × 19) reveals 7 prime building blocks.
Divisible by 2
6840 ends in 0, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
6840 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 18 is a multiple of 9.
Divisible by 10
6840 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 6840 within several notable number theory sequences:
Timeline
Deep dive
How 6840 breaks down
6840 carries 48 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 16560, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101010111000 supports bitwise reasoning, hexadecimal 1AB8 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 6840 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 6840 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (6835–6845) to tune search ranges, and educators feature 6840 in worksheets about factor trees. Its binary footprint of length 13 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 6840 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 6840
Is 6840 a prime number?
6840 is composite with 48 total factors and the prime factorization 2^3 × 3^2 × 5 × 19.
What is the prime factorization of 6840?
It breaks down as 2^3 × 3^2 × 5 × 19, multiplying the primes 2 × 2 × 2 × 3 × 3 × 5 × 19.
How is 6840 represented in binary and hexadecimal?
6840 converts to 1101010111000 in binary and 1AB8 in hexadecimal, which are helpful for computer science applications.
Is 6840 a perfect square, cube, or triangular number?
6840 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 6840?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.