1265
1265 is a odd composite number that follows 1264 and precedes 1266. It is composed of 8 distinct factors: 1, 5, 11, 23, 55, 115, 253, 1265. Its prime factorization can be written as 5 × 11 × 23. 1265 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1265 is represented as 10011110001 in binary and 4F1 in hexadecimal. Historically, it is written as MCCLXV in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (5 × 11 × 23) reveals 3 prime building blocks.
Divisible by 2
1265 ends in 5, so it is odd.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 65 are not divisible by 4.
Divisible by 5
1265 ends in 5, 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 14 is not a multiple of 9.
Divisible by 10
1265 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 1265 within several notable number theory sequences:
Timeline
Deep dive
How 1265 breaks down
1265 carries 8 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 463, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011110001 supports bitwise reasoning, hexadecimal 4F1 aligns with computing notation, and the Roman numeral MCCLXV keeps the encyclopedic tradition alive. These attributes make 1265 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1265 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1260–1270) to tune search ranges, and educators feature 1265 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 1265 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 1265
Is 1265 a prime number?
1265 is composite with 8 total factors and the prime factorization 5 × 11 × 23.
What is the prime factorization of 1265?
It breaks down as 5 × 11 × 23, multiplying the primes 5 × 11 × 23.
How is 1265 represented in binary and hexadecimal?
1265 converts to 10011110001 in binary and 4F1 in hexadecimal, which are helpful for computer science applications.
Is 1265 a perfect square, cube, or triangular number?
1265 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1265?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.