2224
2224 is a even composite number that follows 2223 and precedes 2225. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 139, 278, 556, 1112, 2224. Its prime factorization can be written as 2^4 × 139. 2224 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2224 is represented as 100010110000 in binary and 8B0 in hexadecimal. Historically, it is written as MMCCXXIV in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 139) reveals 5 prime building blocks.
Divisible by 2
2224 ends in 4, so it is even.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
2224 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 10 is not a multiple of 9.
Divisible by 10
2224 does not end in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Deficient classification and digit analytics place 2224 within several notable number theory sequences:
Timeline
Deep dive
How 2224 breaks down
2224 carries 10 distinct factors and a digit signature of 10 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 2116, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100010110000 supports bitwise reasoning, hexadecimal 8B0 aligns with computing notation, and the Roman numeral MMCCXXIV keeps the encyclopedic tradition alive. These attributes make 2224 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2224 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2219–2229) to tune search ranges, and educators feature 2224 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 2224 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 2224
Is 2224 a prime number?
2224 is composite with 10 total factors and the prime factorization 2^4 × 139.
What is the prime factorization of 2224?
It breaks down as 2^4 × 139, multiplying the primes 2 × 2 × 2 × 2 × 139.
How is 2224 represented in binary and hexadecimal?
2224 converts to 100010110000 in binary and 8B0 in hexadecimal, which are helpful for computer science applications.
Is 2224 a perfect square, cube, or triangular number?
2224 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2224?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.