2340
2340 is a even composite number that follows 2339 and precedes 2341. It is composed of 36 distinct factors: 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 180, 195, 234, 260, 390, 468, 585, 780, 1170, 2340. Its prime factorization can be written as 2^2 × 3^2 × 5 × 13. 2340 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2340 is represented as 100100100100 in binary and 924 in hexadecimal. Historically, it is written as MMCCCXL in Roman numerals.
Factor Analysis
36 FactorsProperties
The prime factorization (2^2 × 3^2 × 5 × 13) reveals 6 prime building blocks.
Divisible by 2
2340 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
2340 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 9 is a multiple of 9.
Divisible by 10
2340 ends in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 2340 within several notable number theory sequences:
Timeline
Deep dive
How 2340 breaks down
2340 carries 36 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 5304, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100100100100 supports bitwise reasoning, hexadecimal 924 aligns with computing notation, and the Roman numeral MMCCCXL keeps the encyclopedic tradition alive. These attributes make 2340 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2340 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2335–2345) to tune search ranges, and educators feature 2340 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 2340 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 2340
Is 2340 a prime number?
2340 is composite with 36 total factors and the prime factorization 2^2 × 3^2 × 5 × 13.
What is the prime factorization of 2340?
It breaks down as 2^2 × 3^2 × 5 × 13, multiplying the primes 2 × 2 × 3 × 3 × 5 × 13.
How is 2340 represented in binary and hexadecimal?
2340 converts to 100100100100 in binary and 924 in hexadecimal, which are helpful for computer science applications.
Is 2340 a perfect square, cube, or triangular number?
2340 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2340?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.