1323
1323 is a odd composite number that follows 1322 and precedes 1324. It is composed of 12 distinct factors: 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323. Its prime factorization can be written as 3^3 × 7^2. 1323 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1323 is represented as 10100101011 in binary and 52B in hexadecimal. Historically, it is written as MCCCXXIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3^3 × 7^2) reveals 5 prime building blocks.
Divisible by 2
1323 ends in 3, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 23 are not divisible by 4.
Divisible by 5
1323 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 9 is a multiple of 9.
Divisible by 10
1323 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Deficient classification and digit analytics place 1323 within several notable number theory sequences:
Timeline
Deep dive
How 1323 breaks down
1323 carries 12 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 957, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10100101011 supports bitwise reasoning, hexadecimal 52B aligns with computing notation, and the Roman numeral MCCCXXIII keeps the encyclopedic tradition alive. These attributes make 1323 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1323 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1318–1328) to tune search ranges, and educators feature 1323 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, Deficient numbers) help historians, numerologists, and trivia writers tie 1323 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 1323
Is 1323 a prime number?
1323 is composite with 12 total factors and the prime factorization 3^3 × 7^2.
What is the prime factorization of 1323?
It breaks down as 3^3 × 7^2, multiplying the primes 3 × 3 × 3 × 7 × 7.
How is 1323 represented in binary and hexadecimal?
1323 converts to 10100101011 in binary and 52B in hexadecimal, which are helpful for computer science applications.
Is 1323 a perfect square, cube, or triangular number?
1323 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1323?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.