2540
2540 is a even composite number that follows 2539 and precedes 2541. It is composed of 12 distinct factors: 1, 2, 4, 5, 10, 20, 127, 254, 508, 635, 1270, 2540. Its prime factorization can be written as 2^2 × 5 × 127. 2540 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2540 is represented as 100111101100 in binary and 9EC in hexadecimal. Historically, it is written as MMDXL in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 5 × 127) reveals 4 prime building blocks.
Divisible by 2
2540 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 40 form a multiple of 4.
Divisible by 5
2540 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
2540 ends in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 2540 within several notable number theory sequences:
Timeline
Deep dive
How 2540 breaks down
2540 carries 12 distinct factors and a digit signature of 11 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 2836, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100111101100 supports bitwise reasoning, hexadecimal 9EC aligns with computing notation, and the Roman numeral MMDXL keeps the encyclopedic tradition alive. These attributes make 2540 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2540 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2535–2545) to tune search ranges, and educators feature 2540 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 2540 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 2540
Is 2540 a prime number?
2540 is composite with 12 total factors and the prime factorization 2^2 × 5 × 127.
What is the prime factorization of 2540?
It breaks down as 2^2 × 5 × 127, multiplying the primes 2 × 2 × 5 × 127.
How is 2540 represented in binary and hexadecimal?
2540 converts to 100111101100 in binary and 9EC in hexadecimal, which are helpful for computer science applications.
Is 2540 a perfect square, cube, or triangular number?
2540 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2540?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.