1328
1328 is a even composite number that follows 1327 and precedes 1329. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 83, 166, 332, 664, 1328. Its prime factorization can be written as 2^4 × 83. 1328 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1328 is represented as 10100110000 in binary and 530 in hexadecimal. Historically, it is written as MCCCXXVIII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 83) reveals 5 prime building blocks.
Divisible by 2
1328 ends in 8, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
1328 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 14 is not a multiple of 9.
Divisible by 10
1328 does not end in 0.
Divisible by 11
The alternating digit sum -8 is not a multiple of 11.
Deficient classification and digit analytics place 1328 within several notable number theory sequences:
Timeline
Deep dive
How 1328 breaks down
1328 carries 10 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 1276, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10100110000 supports bitwise reasoning, hexadecimal 530 aligns with computing notation, and the Roman numeral MCCCXXVIII keeps the encyclopedic tradition alive. These attributes make 1328 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1328 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1323–1333) to tune search ranges, and educators feature 1328 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 1328 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 1328
Is 1328 a prime number?
1328 is composite with 10 total factors and the prime factorization 2^4 × 83.
What is the prime factorization of 1328?
It breaks down as 2^4 × 83, multiplying the primes 2 × 2 × 2 × 2 × 83.
How is 1328 represented in binary and hexadecimal?
1328 converts to 10100110000 in binary and 530 in hexadecimal, which are helpful for computer science applications.
Is 1328 a perfect square, cube, or triangular number?
1328 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1328?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.