2640
2640 is a even composite number that follows 2639 and precedes 2641. It is composed of 40 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 33, 40, 44, 48, 55, 60, 66, 80, 88, 110, 120, 132, 165, 176, 220, 240, 264, 330, 440, 528, 660, 880, 1320, 2640. Its prime factorization can be written as 2^4 × 3 × 5 × 11. 2640 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2640 is represented as 101001010000 in binary and A50 in hexadecimal. Historically, it is written as MMDCXL in Roman numerals.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 3 × 5 × 11) reveals 7 prime building blocks.
Divisible by 2
2640 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 40 form a multiple of 4.
Divisible by 5
2640 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
2640 ends in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 2640 within several notable number theory sequences:
Timeline
Deep dive
How 2640 breaks down
2640 carries 40 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 6288, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101001010000 supports bitwise reasoning, hexadecimal A50 aligns with computing notation, and the Roman numeral MMDCXL keeps the encyclopedic tradition alive. These attributes make 2640 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2640 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2635–2645) to tune search ranges, and educators feature 2640 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 2640 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 2640
Is 2640 a prime number?
2640 is composite with 40 total factors and the prime factorization 2^4 × 3 × 5 × 11.
What is the prime factorization of 2640?
It breaks down as 2^4 × 3 × 5 × 11, multiplying the primes 2 × 2 × 2 × 2 × 3 × 5 × 11.
How is 2640 represented in binary and hexadecimal?
2640 converts to 101001010000 in binary and A50 in hexadecimal, which are helpful for computer science applications.
Is 2640 a perfect square, cube, or triangular number?
2640 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2640?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.