2140
2140 is a even composite number that follows 2139 and precedes 2141. It is composed of 12 distinct factors: 1, 2, 4, 5, 10, 20, 107, 214, 428, 535, 1070, 2140. Its prime factorization can be written as 2^2 × 5 × 107. 2140 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2140 is represented as 100001011100 in binary and 85C in hexadecimal. Historically, it is written as MMCXL in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 5 × 107) reveals 4 prime building blocks.
Divisible by 2
2140 ends in 0, so it is even.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
2140 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 7 is not a multiple of 9.
Divisible by 10
2140 ends in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 2140 within several notable number theory sequences:
Timeline
Deep dive
How 2140 breaks down
2140 carries 12 distinct factors and a digit signature of 7 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 2396, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100001011100 supports bitwise reasoning, hexadecimal 85C aligns with computing notation, and the Roman numeral MMCXL keeps the encyclopedic tradition alive. These attributes make 2140 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2140 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2135–2145) to tune search ranges, and educators feature 2140 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 2140 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 2140
Is 2140 a prime number?
2140 is composite with 12 total factors and the prime factorization 2^2 × 5 × 107.
What is the prime factorization of 2140?
It breaks down as 2^2 × 5 × 107, multiplying the primes 2 × 2 × 5 × 107.
How is 2140 represented in binary and hexadecimal?
2140 converts to 100001011100 in binary and 85C in hexadecimal, which are helpful for computer science applications.
Is 2140 a perfect square, cube, or triangular number?
2140 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2140?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.