440
440 is a even composite number that follows 439 and precedes 441. It is composed of 16 distinct factors: 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440. Its prime factorization can be written as 2^3 × 5 × 11. 440 is classified as a abundant number based on the sum of its proper divisors. In computer science, 440 is represented as 110111000 in binary and 1B8 in hexadecimal. Historically, it is written as CDXL in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 5 × 11) reveals 5 prime building blocks.
Divisible by 2
440 ends in 0, so it is even.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
440 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 8 is not a multiple of 9.
Divisible by 10
440 ends in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 440 within several notable number theory sequences:
Timeline
Deep dive
How 440 breaks down
440 carries 16 distinct factors and a digit signature of 8 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 640, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110111000 supports bitwise reasoning, hexadecimal 1B8 aligns with computing notation, and the Roman numeral CDXL keeps the encyclopedic tradition alive. These attributes make 440 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 440 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (435–445) to tune search ranges, and educators feature 440 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, Abundant numbers) help historians, numerologists, and trivia writers tie 440 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 440
Is 440 a prime number?
440 is composite with 16 total factors and the prime factorization 2^3 × 5 × 11.
What is the prime factorization of 440?
It breaks down as 2^3 × 5 × 11, multiplying the primes 2 × 2 × 2 × 5 × 11.
How is 440 represented in binary and hexadecimal?
440 converts to 110111000 in binary and 1B8 in hexadecimal, which are helpful for computer science applications.
Is 440 a perfect square, cube, or triangular number?
440 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 440?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.