3800
3800 is a even composite number that follows 3799 and precedes 3801. It is composed of 24 distinct factors: 1, 2, 4, 5, 8, 10, 19, 20, 25, 38, 40, 50, 76, 95, 100, 152, 190, 200, 380, 475, 760, 950, 1900, 3800. Its prime factorization can be written as 2^3 × 5^2 × 19. 3800 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3800 is represented as 111011011000 in binary and ED8 in hexadecimal. Historically, it is written as MMMDCCC in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^3 × 5^2 × 19) reveals 6 prime building blocks.
Divisible by 2
3800 ends in 0, so it is even.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
3800 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 11 is not a multiple of 9.
Divisible by 10
3800 ends in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Abundant classification and digit analytics place 3800 within several notable number theory sequences:
Timeline
Deep dive
How 3800 breaks down
3800 carries 24 distinct factors and a digit signature of 11 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 5500, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111011011000 supports bitwise reasoning, hexadecimal ED8 aligns with computing notation, and the Roman numeral MMMDCCC keeps the encyclopedic tradition alive. These attributes make 3800 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3800 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3795–3805) to tune search ranges, and educators feature 3800 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 3800 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 3800
Is 3800 a prime number?
3800 is composite with 24 total factors and the prime factorization 2^3 × 5^2 × 19.
What is the prime factorization of 3800?
It breaks down as 2^3 × 5^2 × 19, multiplying the primes 2 × 2 × 2 × 5 × 5 × 19.
How is 3800 represented in binary and hexadecimal?
3800 converts to 111011011000 in binary and ED8 in hexadecimal, which are helpful for computer science applications.
Is 3800 a perfect square, cube, or triangular number?
3800 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3800?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.