3690
3690 is a even composite number that follows 3689 and precedes 3691. It is composed of 24 distinct factors: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 41, 45, 82, 90, 123, 205, 246, 369, 410, 615, 738, 1230, 1845, 3690. Its prime factorization can be written as 2 × 3^2 × 5 × 41. 3690 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3690 is represented as 111001101010 in binary and E6A in hexadecimal. Historically, it is written as MMMDCXC in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2 × 3^2 × 5 × 41) reveals 5 prime building blocks.
Divisible by 2
3690 ends in 0, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 90 are not divisible by 4.
Divisible by 5
3690 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 18 is a multiple of 9.
Divisible by 10
3690 ends in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 3690 within several notable number theory sequences:
Timeline
Deep dive
How 3690 breaks down
3690 carries 24 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 6138, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111001101010 supports bitwise reasoning, hexadecimal E6A aligns with computing notation, and the Roman numeral MMMDCXC keeps the encyclopedic tradition alive. These attributes make 3690 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3690 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3685–3695) to tune search ranges, and educators feature 3690 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 3690 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 3690
Is 3690 a prime number?
3690 is composite with 24 total factors and the prime factorization 2 × 3^2 × 5 × 41.
What is the prime factorization of 3690?
It breaks down as 2 × 3^2 × 5 × 41, multiplying the primes 2 × 3 × 3 × 5 × 41.
How is 3690 represented in binary and hexadecimal?
3690 converts to 111001101010 in binary and E6A in hexadecimal, which are helpful for computer science applications.
Is 3690 a perfect square, cube, or triangular number?
3690 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3690?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.