2742
2742 is a even composite number that follows 2741 and precedes 2743. It is composed of 8 distinct factors: 1, 2, 3, 6, 457, 914, 1371, 2742. Its prime factorization can be written as 2 × 3 × 457. 2742 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2742 is represented as 101010110110 in binary and AB6 in hexadecimal. Historically, it is written as MMDCCXLII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 457) reveals 3 prime building blocks.
Divisible by 2
2742 ends in 2, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 42 are not divisible by 4.
Divisible by 5
2742 does not end in 0 or 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 15 is not a multiple of 9.
Divisible by 10
2742 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 2742 within several notable number theory sequences:
Timeline
Deep dive
How 2742 breaks down
2742 carries 8 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2754, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101010110110 supports bitwise reasoning, hexadecimal AB6 aligns with computing notation, and the Roman numeral MMDCCXLII keeps the encyclopedic tradition alive. These attributes make 2742 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2742 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2737–2747) to tune search ranges, and educators feature 2742 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 2742 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 2742
Is 2742 a prime number?
2742 is composite with 8 total factors and the prime factorization 2 × 3 × 457.
What is the prime factorization of 2742?
It breaks down as 2 × 3 × 457, multiplying the primes 2 × 3 × 457.
How is 2742 represented in binary and hexadecimal?
2742 converts to 101010110110 in binary and AB6 in hexadecimal, which are helpful for computer science applications.
Is 2742 a perfect square, cube, or triangular number?
2742 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2742?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.