1310
1310 is a even composite number that follows 1309 and precedes 1311. It is composed of 8 distinct factors: 1, 2, 5, 10, 131, 262, 655, 1310. Its prime factorization can be written as 2 × 5 × 131. 1310 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1310 is represented as 10100011110 in binary and 51E in hexadecimal. Historically, it is written as MCCCX in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 5 × 131) reveals 3 prime building blocks.
Divisible by 2
1310 ends in 0, so it is even.
Divisible by 3
The digit sum 5 is not a multiple of 3.
Divisible by 4
The last two digits 10 are not divisible by 4.
Divisible by 5
1310 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 5 is not a multiple of 9.
Divisible by 10
1310 ends in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Deficient classification and digit analytics place 1310 within several notable number theory sequences:
Timeline
Deep dive
How 1310 breaks down
1310 carries 8 distinct factors and a digit signature of 5 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 1066, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10100011110 supports bitwise reasoning, hexadecimal 51E aligns with computing notation, and the Roman numeral MCCCX keeps the encyclopedic tradition alive. These attributes make 1310 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1310 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1305–1315) to tune search ranges, and educators feature 1310 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 1310 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 1310
Is 1310 a prime number?
1310 is composite with 8 total factors and the prime factorization 2 × 5 × 131.
What is the prime factorization of 1310?
It breaks down as 2 × 5 × 131, multiplying the primes 2 × 5 × 131.
How is 1310 represented in binary and hexadecimal?
1310 converts to 10100011110 in binary and 51E in hexadecimal, which are helpful for computer science applications.
Is 1310 a perfect square, cube, or triangular number?
1310 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1310?
The digits sum to 5, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.