1275
1275 is a odd composite number that follows 1274 and precedes 1276. It is composed of 12 distinct factors: 1, 3, 5, 15, 17, 25, 51, 75, 85, 255, 425, 1275. Its prime factorization can be written as 3 × 5^2 × 17. 1275 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1275 is represented as 10011111011 in binary and 4FB in hexadecimal. Historically, it is written as MCCLXXV in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
12 FactorsProperties
The prime factorization (3 × 5^2 × 17) reveals 4 prime building blocks.
Divisible by 2
1275 ends in 5, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 75 are not divisible by 4.
Divisible by 5
1275 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 15 is not a multiple of 9.
Divisible by 10
1275 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 1275 within several notable number theory sequences:
Timeline
Deep dive
How 1275 breaks down
1275 carries 12 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 957, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011111011 supports bitwise reasoning, hexadecimal 4FB aligns with computing notation, and the Roman numeral MCCLXXV keeps the encyclopedic tradition alive. These attributes make 1275 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1275 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1270–1280) to tune search ranges, and educators feature 1275 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, Triangular numbers) help historians, numerologists, and trivia writers tie 1275 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 1275
Is 1275 a prime number?
1275 is composite with 12 total factors and the prime factorization 3 × 5^2 × 17.
What is the prime factorization of 1275?
It breaks down as 3 × 5^2 × 17, multiplying the primes 3 × 5 × 5 × 17.
How is 1275 represented in binary and hexadecimal?
1275 converts to 10011111011 in binary and 4FB in hexadecimal, which are helpful for computer science applications.
Is 1275 a perfect square, cube, or triangular number?
1275 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 1275?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.