3663
3663 is a odd composite number that follows 3662 and precedes 3664. It is composed of 12 distinct factors: 1, 3, 9, 11, 33, 37, 99, 111, 333, 407, 1221, 3663. Its prime factorization can be written as 3^2 × 11 × 37. 3663 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3663 is represented as 111001001111 in binary and E4F in hexadecimal. Historically, it is written as MMMDCLXIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3^2 × 11 × 37) reveals 4 prime building blocks.
Divisible by 2
3663 ends in 3, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 63 are not divisible by 4.
Divisible by 5
3663 does not end in 0 or 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
3663 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 3663 within several notable number theory sequences:
Timeline
Deep dive
How 3663 breaks down
3663 carries 12 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 2265, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111001001111 supports bitwise reasoning, hexadecimal E4F aligns with computing notation, and the Roman numeral MMMDCLXIII keeps the encyclopedic tradition alive. These attributes make 3663 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3663 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3658–3668) to tune search ranges, and educators feature 3663 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 3663 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 3663
Is 3663 a prime number?
3663 is composite with 12 total factors and the prime factorization 3^2 × 11 × 37.
What is the prime factorization of 3663?
It breaks down as 3^2 × 11 × 37, multiplying the primes 3 × 3 × 11 × 37.
How is 3663 represented in binary and hexadecimal?
3663 converts to 111001001111 in binary and E4F in hexadecimal, which are helpful for computer science applications.
Is 3663 a perfect square, cube, or triangular number?
3663 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3663?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.