3645
3645 is a odd composite number that follows 3644 and precedes 3646. It is composed of 14 distinct factors: 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 729, 1215, 3645. Its prime factorization can be written as 3^6 × 5. 3645 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3645 is represented as 111000111101 in binary and E3D in hexadecimal. Historically, it is written as MMMDCXLV in Roman numerals.
Factor Analysis
14 FactorsProperties
The prime factorization (3^6 × 5) reveals 7 prime building blocks.
Divisible by 2
3645 ends in 5, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 45 are not divisible by 4.
Divisible by 5
3645 ends in 5, 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 18 is a multiple of 9.
Divisible by 10
3645 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Deficient classification and digit analytics place 3645 within several notable number theory sequences:
Timeline
Deep dive
How 3645 breaks down
3645 carries 14 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 2913, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111000111101 supports bitwise reasoning, hexadecimal E3D aligns with computing notation, and the Roman numeral MMMDCXLV keeps the encyclopedic tradition alive. These attributes make 3645 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3645 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3640–3650) to tune search ranges, and educators feature 3645 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, Deficient numbers) help historians, numerologists, and trivia writers tie 3645 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 3645
Is 3645 a prime number?
3645 is composite with 14 total factors and the prime factorization 3^6 × 5.
What is the prime factorization of 3645?
It breaks down as 3^6 × 5, multiplying the primes 3 × 3 × 3 × 3 × 3 × 3 × 5.
How is 3645 represented in binary and hexadecimal?
3645 converts to 111000111101 in binary and E3D in hexadecimal, which are helpful for computer science applications.
Is 3645 a perfect square, cube, or triangular number?
3645 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3645?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.