441
441 is a odd composite number that follows 440 and precedes 442. It is composed of 9 distinct factors: 1, 3, 7, 9, 21, 49, 63, 147, 441. Its prime factorization can be written as 3^2 × 7^2. 441 is classified as a deficient number based on the sum of its proper divisors. In computer science, 441 is represented as 110111001 in binary and 1B9 in hexadecimal. Historically, it is written as CDXLI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
9 FactorsProperties
The prime factorization (3^2 × 7^2) reveals 4 prime building blocks.
Divisible by 2
441 ends in 1, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 41 are not divisible by 4.
Divisible by 5
441 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 9 is a multiple of 9.
Divisible by 10
441 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Deficient classification and digit analytics place 441 within several notable number theory sequences:
Timeline
Deep dive
How 441 breaks down
441 carries 9 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 300, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110111001 supports bitwise reasoning, hexadecimal 1B9 aligns with computing notation, and the Roman numeral CDXLI keeps the encyclopedic tradition alive. These attributes make 441 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 441 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (436–446) to tune search ranges, and educators feature 441 in worksheets about factor trees. Its binary footprint of length 9 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers, Perfect squares) help historians, numerologists, and trivia writers tie 441 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 441
Is 441 a prime number?
441 is composite with 9 total factors and the prime factorization 3^2 × 7^2.
What is the prime factorization of 441?
It breaks down as 3^2 × 7^2, multiplying the primes 3 × 3 × 7 × 7.
How is 441 represented in binary and hexadecimal?
441 converts to 110111001 in binary and 1B9 in hexadecimal, which are helpful for computer science applications.
Is 441 a perfect square, cube, or triangular number?
441 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 441?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.