840
840 is a even composite number that follows 839 and precedes 841. It is composed of 32 distinct factors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840. Its prime factorization can be written as 2^3 × 3 × 5 × 7. 840 is classified as a abundant number based on the sum of its proper divisors. In computer science, 840 is represented as 1101001000 in binary and 348 in hexadecimal. Historically, it is written as DCCCXL in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 3 × 5 × 7) reveals 6 prime building blocks.
Divisible by 2
840 ends in 0, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
840 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 12 is not a multiple of 9.
Divisible by 10
840 ends in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 840 within several notable number theory sequences:
Timeline
Deep dive
How 840 breaks down
840 carries 32 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 2040, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101001000 supports bitwise reasoning, hexadecimal 348 aligns with computing notation, and the Roman numeral DCCCXL keeps the encyclopedic tradition alive. These attributes make 840 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 840 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (835–845) to tune search ranges, and educators feature 840 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 840 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 840
Is 840 a prime number?
840 is composite with 32 total factors and the prime factorization 2^3 × 3 × 5 × 7.
What is the prime factorization of 840?
It breaks down as 2^3 × 3 × 5 × 7, multiplying the primes 2 × 2 × 2 × 3 × 5 × 7.
How is 840 represented in binary and hexadecimal?
840 converts to 1101001000 in binary and 348 in hexadecimal, which are helpful for computer science applications.
Is 840 a perfect square, cube, or triangular number?
840 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 840?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.