1321
1321 is a odd prime number that follows 1320 and precedes 1322. As a prime number, 1321 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 1321. 1321 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1321 is represented as 10100101001 in binary and 529 in hexadecimal. Historically, it is written as MCCCXXI in Roman numerals.
Factor Analysis
2 FactorsProperties
1321 is prime, so its only factors are 1 and 1321.
Divisible by 2
1321 ends in 1, so it is odd.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 21 are not divisible by 4.
Divisible by 5
1321 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 7 is not a multiple of 9.
Divisible by 10
1321 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Deficient classification and digit analytics place 1321 within several notable number theory sequences:
Timeline
Deep dive
How 1321 breaks down
1321 carries 2 distinct factors and a digit signature of 7 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10100101001 supports bitwise reasoning, hexadecimal 529 aligns with computing notation, and the Roman numeral MCCCXXI keeps the encyclopedic tradition alive. These attributes make 1321 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1321 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1316–1326) to tune search ranges, and educators feature 1321 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 1321 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 1321
Is 1321 a prime number?
1321 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 1321?
1321 is already prime, so the factorization is simply 1321.
How is 1321 represented in binary and hexadecimal?
1321 converts to 10100101001 in binary and 529 in hexadecimal, which are helpful for computer science applications.
Is 1321 a perfect square, cube, or triangular number?
1321 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1321?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.