1307
1307 is a odd prime number that follows 1306 and precedes 1308. As a prime number, 1307 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 1307. 1307 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1307 is represented as 10100011011 in binary and 51B in hexadecimal. Historically, it is written as MCCCVII in Roman numerals.
Factor Analysis
2 FactorsProperties
1307 is prime, so its only factors are 1 and 1307.
Divisible by 2
1307 ends in 7, so it is odd.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 07 are not divisible by 4.
Divisible by 5
1307 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 11 is not a multiple of 9.
Divisible by 10
1307 does not end in 0.
Divisible by 11
The alternating digit sum -9 is not a multiple of 11.
Deficient classification and digit analytics place 1307 within several notable number theory sequences:
Timeline
Deep dive
How 1307 breaks down
1307 carries 2 distinct factors and a digit signature of 11 (2 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 10100011011 supports bitwise reasoning, hexadecimal 51B aligns with computing notation, and the Roman numeral MCCCVII keeps the encyclopedic tradition alive. These attributes make 1307 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1307 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1302–1312) to tune search ranges, and educators feature 1307 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 1307 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 1307
Is 1307 a prime number?
1307 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 1307?
1307 is already prime, so the factorization is simply 1307.
How is 1307 represented in binary and hexadecimal?
1307 converts to 10100011011 in binary and 51B in hexadecimal, which are helpful for computer science applications.
Is 1307 a perfect square, cube, or triangular number?
1307 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1307?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.