1078
1078 is a even composite number that follows 1077 and precedes 1079. It is composed of 12 distinct factors: 1, 2, 7, 11, 14, 22, 49, 77, 98, 154, 539, 1078. Its prime factorization can be written as 2 × 7^2 × 11. 1078 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1078 is represented as 10000110110 in binary and 436 in hexadecimal. Historically, it is written as MLXXVIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 7^2 × 11) reveals 4 prime building blocks.
Divisible by 2
1078 ends in 8, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 78 are not divisible by 4.
Divisible by 5
1078 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 16 is not a multiple of 9.
Divisible by 10
1078 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 1078 within several notable number theory sequences:
Timeline
Deep dive
How 1078 breaks down
1078 carries 12 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 974, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000110110 supports bitwise reasoning, hexadecimal 436 aligns with computing notation, and the Roman numeral MLXXVIII keeps the encyclopedic tradition alive. These attributes make 1078 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1078 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1073–1083) to tune search ranges, and educators feature 1078 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 1078 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 1078
Is 1078 a prime number?
1078 is composite with 12 total factors and the prime factorization 2 × 7^2 × 11.
What is the prime factorization of 1078?
It breaks down as 2 × 7^2 × 11, multiplying the primes 2 × 7 × 7 × 11.
How is 1078 represented in binary and hexadecimal?
1078 converts to 10000110110 in binary and 436 in hexadecimal, which are helpful for computer science applications.
Is 1078 a perfect square, cube, or triangular number?
1078 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1078?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.