3640
3640 is a even composite number that follows 3639 and precedes 3641. It is composed of 32 distinct factors: 1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 26, 28, 35, 40, 52, 56, 65, 70, 91, 104, 130, 140, 182, 260, 280, 364, 455, 520, 728, 910, 1820, 3640. Its prime factorization can be written as 2^3 × 5 × 7 × 13. 3640 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3640 is represented as 111000111000 in binary and E38 in hexadecimal. Historically, it is written as MMMDCXL in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 5 × 7 × 13) reveals 6 prime building blocks.
Divisible by 2
3640 ends in 0, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
3640 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 13 is not a multiple of 9.
Divisible by 10
3640 ends in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 3640 within several notable number theory sequences:
Timeline
Deep dive
How 3640 breaks down
3640 carries 32 distinct factors and a digit signature of 13 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 6440, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111000111000 supports bitwise reasoning, hexadecimal E38 aligns with computing notation, and the Roman numeral MMMDCXL keeps the encyclopedic tradition alive. These attributes make 3640 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3640 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3635–3645) to tune search ranges, and educators feature 3640 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 3640 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 3640
Is 3640 a prime number?
3640 is composite with 32 total factors and the prime factorization 2^3 × 5 × 7 × 13.
What is the prime factorization of 3640?
It breaks down as 2^3 × 5 × 7 × 13, multiplying the primes 2 × 2 × 2 × 5 × 7 × 13.
How is 3640 represented in binary and hexadecimal?
3640 converts to 111000111000 in binary and E38 in hexadecimal, which are helpful for computer science applications.
Is 3640 a perfect square, cube, or triangular number?
3640 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3640?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.