3224
3224 is a even composite number that follows 3223 and precedes 3225. It is composed of 16 distinct factors: 1, 2, 4, 8, 13, 26, 31, 52, 62, 104, 124, 248, 403, 806, 1612, 3224. Its prime factorization can be written as 2^3 × 13 × 31. 3224 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3224 is represented as 110010011000 in binary and C98 in hexadecimal. Historically, it is written as MMMCCXXIV in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 13 × 31) reveals 5 prime building blocks.
Divisible by 2
3224 ends in 4, so it is even.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
3224 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 11 is not a multiple of 9.
Divisible by 10
3224 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 3224 within several notable number theory sequences:
Timeline
Deep dive
How 3224 breaks down
3224 carries 16 distinct factors and a digit signature of 11 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 3496, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010011000 supports bitwise reasoning, hexadecimal C98 aligns with computing notation, and the Roman numeral MMMCCXXIV keeps the encyclopedic tradition alive. These attributes make 3224 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3224 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3219–3229) to tune search ranges, and educators feature 3224 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, Abundant numbers) help historians, numerologists, and trivia writers tie 3224 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 3224
Is 3224 a prime number?
3224 is composite with 16 total factors and the prime factorization 2^3 × 13 × 31.
What is the prime factorization of 3224?
It breaks down as 2^3 × 13 × 31, multiplying the primes 2 × 2 × 2 × 13 × 31.
How is 3224 represented in binary and hexadecimal?
3224 converts to 110010011000 in binary and C98 in hexadecimal, which are helpful for computer science applications.
Is 3224 a perfect square, cube, or triangular number?
3224 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3224?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.