1278
1278 is a even composite number that follows 1277 and precedes 1279. It is composed of 12 distinct factors: 1, 2, 3, 6, 9, 18, 71, 142, 213, 426, 639, 1278. Its prime factorization can be written as 2 × 3^2 × 71. 1278 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1278 is represented as 10011111110 in binary and 4FE in hexadecimal. Historically, it is written as MCCLXXVIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3^2 × 71) reveals 4 prime building blocks.
Divisible by 2
1278 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 78 are not divisible by 4.
Divisible by 5
1278 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 18 is a multiple of 9.
Divisible by 10
1278 does not end in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 1278 within several notable number theory sequences:
Timeline
Deep dive
How 1278 breaks down
1278 carries 12 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1530, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011111110 supports bitwise reasoning, hexadecimal 4FE aligns with computing notation, and the Roman numeral MCCLXXVIII keeps the encyclopedic tradition alive. These attributes make 1278 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1278 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1273–1283) to tune search ranges, and educators feature 1278 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, Abundant numbers) help historians, numerologists, and trivia writers tie 1278 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 1278
Is 1278 a prime number?
1278 is composite with 12 total factors and the prime factorization 2 × 3^2 × 71.
What is the prime factorization of 1278?
It breaks down as 2 × 3^2 × 71, multiplying the primes 2 × 3 × 3 × 71.
How is 1278 represented in binary and hexadecimal?
1278 converts to 10011111110 in binary and 4FE in hexadecimal, which are helpful for computer science applications.
Is 1278 a perfect square, cube, or triangular number?
1278 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1278?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.