2730
2730 is a even composite number that follows 2729 and precedes 2731. It is composed of 32 distinct factors: 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 21, 26, 30, 35, 39, 42, 65, 70, 78, 91, 105, 130, 182, 195, 210, 273, 390, 455, 546, 910, 1365, 2730. Its prime factorization can be written as 2 × 3 × 5 × 7 × 13. 2730 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2730 is represented as 101010101010 in binary and AAA in hexadecimal. Historically, it is written as MMDCCXXX in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2 × 3 × 5 × 7 × 13) reveals 5 prime building blocks.
Divisible by 2
2730 ends in 0, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 30 are not divisible by 4.
Divisible by 5
2730 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 12 is not a multiple of 9.
Divisible by 10
2730 ends in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 2730 within several notable number theory sequences:
Timeline
Deep dive
How 2730 breaks down
2730 carries 32 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 5334, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101010101010 supports bitwise reasoning, hexadecimal AAA aligns with computing notation, and the Roman numeral MMDCCXXX keeps the encyclopedic tradition alive. These attributes make 2730 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2730 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2725–2735) to tune search ranges, and educators feature 2730 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 2730 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 2730
Is 2730 a prime number?
2730 is composite with 32 total factors and the prime factorization 2 × 3 × 5 × 7 × 13.
What is the prime factorization of 2730?
It breaks down as 2 × 3 × 5 × 7 × 13, multiplying the primes 2 × 3 × 5 × 7 × 13.
How is 2730 represented in binary and hexadecimal?
2730 converts to 101010101010 in binary and AAA in hexadecimal, which are helpful for computer science applications.
Is 2730 a perfect square, cube, or triangular number?
2730 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2730?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.