1077
1077 is a odd composite number that follows 1076 and precedes 1078. It is composed of 4 distinct factors: 1, 3, 359, 1077. Its prime factorization can be written as 3 × 359. 1077 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1077 is represented as 10000110101 in binary and 435 in hexadecimal. Historically, it is written as MLXXVII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (3 × 359) reveals 2 prime building blocks.
Divisible by 2
1077 ends in 7, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 77 are not divisible by 4.
Divisible by 5
1077 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 15 is not a multiple of 9.
Divisible by 10
1077 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 1077 within several notable number theory sequences:
Timeline
Deep dive
How 1077 breaks down
1077 carries 4 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 363, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000110101 supports bitwise reasoning, hexadecimal 435 aligns with computing notation, and the Roman numeral MLXXVII keeps the encyclopedic tradition alive. These attributes make 1077 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1077 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1072–1082) to tune search ranges, and educators feature 1077 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 1077 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 1077
Is 1077 a prime number?
1077 is composite with 4 total factors and the prime factorization 3 × 359.
What is the prime factorization of 1077?
It breaks down as 3 × 359, multiplying the primes 3 × 359.
How is 1077 represented in binary and hexadecimal?
1077 converts to 10000110101 in binary and 435 in hexadecimal, which are helpful for computer science applications.
Is 1077 a perfect square, cube, or triangular number?
1077 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1077?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.