7980
7980 is a even composite number that follows 7979 and precedes 7981. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 28, 30, 35, 38, 42, 57, 60, 70, 76, 84, 95, 105, 114, 133, 140, 190, 210, 228, 266, 285, 380, 399, 420, 532, 570, 665, 798, 1140, 1330, 1596, 1995, 2660, 3990, 7980. Its prime factorization can be written as 2^2 × 3 × 5 × 7 × 19. 7980 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7980 is represented as 1111100101100 in binary and 1F2C in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^2 × 3 × 5 × 7 × 19) reveals 6 prime building blocks.
Divisible by 2
7980 ends in 0, so it is even.
Divisible by 3
The digit sum 24 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
7980 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 24 is not a multiple of 9.
Divisible by 10
7980 ends in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 7980 within several notable number theory sequences:
Timeline
Deep dive
How 7980 breaks down
7980 carries 48 distinct factors and a digit signature of 24 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 18900, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111100101100 supports bitwise reasoning, hexadecimal 1F2C aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7980 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7980 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7975–7985) to tune search ranges, and educators feature 7980 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 7980 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 7980
Is 7980 a prime number?
7980 is composite with 48 total factors and the prime factorization 2^2 × 3 × 5 × 7 × 19.
What is the prime factorization of 7980?
It breaks down as 2^2 × 3 × 5 × 7 × 19, multiplying the primes 2 × 2 × 3 × 5 × 7 × 19.
How is 7980 represented in binary and hexadecimal?
7980 converts to 1111100101100 in binary and 1F2C in hexadecimal, which are helpful for computer science applications.
Is 7980 a perfect square, cube, or triangular number?
7980 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7980?
The digits sum to 24, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.