3980
3980 is a even composite number that follows 3979 and precedes 3981. It is composed of 12 distinct factors: 1, 2, 4, 5, 10, 20, 199, 398, 796, 995, 1990, 3980. Its prime factorization can be written as 2^2 × 5 × 199. 3980 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3980 is represented as 111110001100 in binary and F8C in hexadecimal. Historically, it is written as MMMCMLXXX in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 5 × 199) reveals 4 prime building blocks.
Divisible by 2
3980 ends in 0, so it is even.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
3980 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 20 is not a multiple of 9.
Divisible by 10
3980 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 3980 within several notable number theory sequences:
Timeline
Deep dive
How 3980 breaks down
3980 carries 12 distinct factors and a digit signature of 20 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 4420, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111110001100 supports bitwise reasoning, hexadecimal F8C aligns with computing notation, and the Roman numeral MMMCMLXXX keeps the encyclopedic tradition alive. These attributes make 3980 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3980 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3975–3985) to tune search ranges, and educators feature 3980 in worksheets about factor trees. Its binary footprint of length 12 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 3980 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 3980
Is 3980 a prime number?
3980 is composite with 12 total factors and the prime factorization 2^2 × 5 × 199.
What is the prime factorization of 3980?
It breaks down as 2^2 × 5 × 199, multiplying the primes 2 × 2 × 5 × 199.
How is 3980 represented in binary and hexadecimal?
3980 converts to 111110001100 in binary and F8C in hexadecimal, which are helpful for computer science applications.
Is 3980 a perfect square, cube, or triangular number?
3980 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3980?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.