2100
2100 is a even composite number that follows 2099 and precedes 2101. It is composed of 36 distinct factors: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100. Its prime factorization can be written as 2^2 × 3 × 5^2 × 7. 2100 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2100 is represented as 100000110100 in binary and 834 in hexadecimal. Historically, it is written as MMC in Roman numerals.
Factor Analysis
36 FactorsProperties
The prime factorization (2^2 × 3 × 5^2 × 7) reveals 6 prime building blocks.
Divisible by 2
2100 ends in 0, so it is even.
Divisible by 3
The digit sum 3 is a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
2100 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 3 is not a multiple of 9.
Divisible by 10
2100 ends in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 2100 within several notable number theory sequences:
Timeline
Deep dive
How 2100 breaks down
2100 carries 36 distinct factors and a digit signature of 3 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 4844, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100000110100 supports bitwise reasoning, hexadecimal 834 aligns with computing notation, and the Roman numeral MMC keeps the encyclopedic tradition alive. These attributes make 2100 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2100 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2095–2105) to tune search ranges, and educators feature 2100 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 2100 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 2100
Is 2100 a prime number?
2100 is composite with 36 total factors and the prime factorization 2^2 × 3 × 5^2 × 7.
What is the prime factorization of 2100?
It breaks down as 2^2 × 3 × 5^2 × 7, multiplying the primes 2 × 2 × 3 × 5 × 5 × 7.
How is 2100 represented in binary and hexadecimal?
2100 converts to 100000110100 in binary and 834 in hexadecimal, which are helpful for computer science applications.
Is 2100 a perfect square, cube, or triangular number?
2100 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2100?
The digits sum to 3, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.