7820
7820 is a even composite number that follows 7819 and precedes 7821. It is composed of 24 distinct factors: 1, 2, 4, 5, 10, 17, 20, 23, 34, 46, 68, 85, 92, 115, 170, 230, 340, 391, 460, 782, 1564, 1955, 3910, 7820. Its prime factorization can be written as 2^2 × 5 × 17 × 23. 7820 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7820 is represented as 1111010001100 in binary and 1E8C in hexadecimal.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 5 × 17 × 23) reveals 5 prime building blocks.
Divisible by 2
7820 ends in 0, so it is even.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
7820 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 17 is not a multiple of 9.
Divisible by 10
7820 ends in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 7820 within several notable number theory sequences:
Timeline
Deep dive
How 7820 breaks down
7820 carries 24 distinct factors and a digit signature of 17 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 10324, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111010001100 supports bitwise reasoning, hexadecimal 1E8C aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7820 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7820 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7815–7825) to tune search ranges, and educators feature 7820 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 7820 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 7820
Is 7820 a prime number?
7820 is composite with 24 total factors and the prime factorization 2^2 × 5 × 17 × 23.
What is the prime factorization of 7820?
It breaks down as 2^2 × 5 × 17 × 23, multiplying the primes 2 × 2 × 5 × 17 × 23.
How is 7820 represented in binary and hexadecimal?
7820 converts to 1111010001100 in binary and 1E8C in hexadecimal, which are helpful for computer science applications.
Is 7820 a perfect square, cube, or triangular number?
7820 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7820?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.