7920
7920 is a even composite number that follows 7919 and precedes 7921. It is composed of 60 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 99, 110, 120, 132, 144, 165, 176, 180, 198, 220, 240, 264, 330, 360, 396, 440, 495, 528, 660, 720, 792, 880, 990, 1320, 1584, 1980, 2640, 3960, 7920. Its prime factorization can be written as 2^4 × 3^2 × 5 × 11. 7920 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7920 is represented as 1111011110000 in binary and 1EF0 in hexadecimal.
Factor Analysis
60 FactorsProperties
The prime factorization (2^4 × 3^2 × 5 × 11) reveals 8 prime building blocks.
Divisible by 2
7920 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 20 form a multiple of 4.
Divisible by 5
7920 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
7920 ends in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 7920 within several notable number theory sequences:
Timeline
Deep dive
How 7920 breaks down
7920 carries 60 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 21096, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111011110000 supports bitwise reasoning, hexadecimal 1EF0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7920 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7920 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7915–7925) to tune search ranges, and educators feature 7920 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 7920 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 7920
Is 7920 a prime number?
7920 is composite with 60 total factors and the prime factorization 2^4 × 3^2 × 5 × 11.
What is the prime factorization of 7920?
It breaks down as 2^4 × 3^2 × 5 × 11, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 5 × 11.
How is 7920 represented in binary and hexadecimal?
7920 converts to 1111011110000 in binary and 1EF0 in hexadecimal, which are helpful for computer science applications.
Is 7920 a perfect square, cube, or triangular number?
7920 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7920?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.