224
224 is a even composite number that follows 223 and precedes 225. It is composed of 12 distinct factors: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224. Its prime factorization can be written as 2^5 × 7. 224 is classified as a abundant number based on the sum of its proper divisors. In computer science, 224 is represented as 11100000 in binary and E0 in hexadecimal. Historically, it is written as CCXXIV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^5 × 7) reveals 6 prime building blocks.
Divisible by 2
224 ends in 4, so it is even.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
224 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 8 is not a multiple of 9.
Divisible by 10
224 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 224 within several notable number theory sequences:
Timeline
Deep dive
How 224 breaks down
224 carries 12 distinct factors and a digit signature of 8 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 280, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100000 supports bitwise reasoning, hexadecimal E0 aligns with computing notation, and the Roman numeral CCXXIV keeps the encyclopedic tradition alive. These attributes make 224 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 224 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (219–229) to tune search ranges, and educators feature 224 in worksheets about factor trees. Its binary footprint of length 8 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 224 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 224
Is 224 a prime number?
224 is composite with 12 total factors and the prime factorization 2^5 × 7.
What is the prime factorization of 224?
It breaks down as 2^5 × 7, multiplying the primes 2 × 2 × 2 × 2 × 2 × 7.
How is 224 represented in binary and hexadecimal?
224 converts to 11100000 in binary and E0 in hexadecimal, which are helpful for computer science applications.
Is 224 a perfect square, cube, or triangular number?
224 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 224?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.