2724
2724 is a even composite number that follows 2723 and precedes 2725. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 12, 227, 454, 681, 908, 1362, 2724. Its prime factorization can be written as 2^2 × 3 × 227. 2724 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2724 is represented as 101010100100 in binary and AA4 in hexadecimal. Historically, it is written as MMDCCXXIV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3 × 227) reveals 4 prime building blocks.
Divisible by 2
2724 ends in 4, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
2724 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
2724 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Abundant classification and digit analytics place 2724 within several notable number theory sequences:
Timeline
Deep dive
How 2724 breaks down
2724 carries 12 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 3660, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101010100100 supports bitwise reasoning, hexadecimal AA4 aligns with computing notation, and the Roman numeral MMDCCXXIV keeps the encyclopedic tradition alive. These attributes make 2724 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2724 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2719–2729) to tune search ranges, and educators feature 2724 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 2724 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 2724
Is 2724 a prime number?
2724 is composite with 12 total factors and the prime factorization 2^2 × 3 × 227.
What is the prime factorization of 2724?
It breaks down as 2^2 × 3 × 227, multiplying the primes 2 × 2 × 3 × 227.
How is 2724 represented in binary and hexadecimal?
2724 converts to 101010100100 in binary and AA4 in hexadecimal, which are helpful for computer science applications.
Is 2724 a perfect square, cube, or triangular number?
2724 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2724?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.