1309
1309 is a odd composite number that follows 1308 and precedes 1310. It is composed of 8 distinct factors: 1, 7, 11, 17, 77, 119, 187, 1309. Its prime factorization can be written as 7 × 11 × 17. 1309 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1309 is represented as 10100011101 in binary and 51D in hexadecimal. Historically, it is written as MCCCIX in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (7 × 11 × 17) reveals 3 prime building blocks.
Divisible by 2
1309 ends in 9, so it is odd.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 09 are not divisible by 4.
Divisible by 5
1309 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 13 is not a multiple of 9.
Divisible by 10
1309 does not end in 0.
Divisible by 11
The alternating digit sum -11 is a multiple of 11.
Deficient classification and digit analytics place 1309 within several notable number theory sequences:
Timeline
Deep dive
How 1309 breaks down
1309 carries 8 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 419, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10100011101 supports bitwise reasoning, hexadecimal 51D aligns with computing notation, and the Roman numeral MCCCIX keeps the encyclopedic tradition alive. These attributes make 1309 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1309 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1304–1314) to tune search ranges, and educators feature 1309 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 1309 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 1309
Is 1309 a prime number?
1309 is composite with 8 total factors and the prime factorization 7 × 11 × 17.
What is the prime factorization of 1309?
It breaks down as 7 × 11 × 17, multiplying the primes 7 × 11 × 17.
How is 1309 represented in binary and hexadecimal?
1309 converts to 10100011101 in binary and 51D in hexadecimal, which are helpful for computer science applications.
Is 1309 a perfect square, cube, or triangular number?
1309 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1309?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.