1224
1224 is a even composite number that follows 1223 and precedes 1225. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224. Its prime factorization can be written as 2^3 × 3^2 × 17. 1224 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1224 is represented as 10011001000 in binary and 4C8 in hexadecimal. Historically, it is written as MCCXXIV in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^3 × 3^2 × 17) reveals 6 prime building blocks.
Divisible by 2
1224 ends in 4, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
1224 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 9 is a multiple of 9.
Divisible by 10
1224 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 1224 within several notable number theory sequences:
Timeline
Deep dive
How 1224 breaks down
1224 carries 24 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 2286, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011001000 supports bitwise reasoning, hexadecimal 4C8 aligns with computing notation, and the Roman numeral MCCXXIV keeps the encyclopedic tradition alive. These attributes make 1224 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1224 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1219–1229) to tune search ranges, and educators feature 1224 in worksheets about factor trees. Its binary footprint of length 11 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 1224 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 1224
Is 1224 a prime number?
1224 is composite with 24 total factors and the prime factorization 2^3 × 3^2 × 17.
What is the prime factorization of 1224?
It breaks down as 2^3 × 3^2 × 17, multiplying the primes 2 × 2 × 2 × 3 × 3 × 17.
How is 1224 represented in binary and hexadecimal?
1224 converts to 10011001000 in binary and 4C8 in hexadecimal, which are helpful for computer science applications.
Is 1224 a perfect square, cube, or triangular number?
1224 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1224?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.