324
324 is a even composite number that follows 323 and precedes 325. It is composed of 15 distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324. Its prime factorization can be written as 2^2 × 3^4. 324 is classified as a abundant number based on the sum of its proper divisors. In computer science, 324 is represented as 101000100 in binary and 144 in hexadecimal. Historically, it is written as CCCXXIV in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
15 FactorsProperties
The prime factorization (2^2 × 3^4) reveals 6 prime building blocks.
Divisible by 2
324 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
324 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
324 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 324 within several notable number theory sequences:
Timeline
Deep dive
How 324 breaks down
324 carries 15 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 523, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101000100 supports bitwise reasoning, hexadecimal 144 aligns with computing notation, and the Roman numeral CCCXXIV keeps the encyclopedic tradition alive. These attributes make 324 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 324 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (319–329) to tune search ranges, and educators feature 324 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, Perfect squares) help historians, numerologists, and trivia writers tie 324 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 324
Is 324 a prime number?
324 is composite with 15 total factors and the prime factorization 2^2 × 3^4.
What is the prime factorization of 324?
It breaks down as 2^2 × 3^4, multiplying the primes 2 × 2 × 3 × 3 × 3 × 3.
How is 324 represented in binary and hexadecimal?
324 converts to 101000100 in binary and 144 in hexadecimal, which are helpful for computer science applications.
Is 324 a perfect square, cube, or triangular number?
324 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 324?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.