767
767 is a odd composite number that follows 766 and precedes 768. It is composed of 4 distinct factors: 1, 13, 59, 767. Its prime factorization can be written as 13 × 59. 767 is classified as a deficient number based on the sum of its proper divisors. In computer science, 767 is represented as 1011111111 in binary and 2FF in hexadecimal. Historically, it is written as DCCLXVII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (13 × 59) reveals 2 prime building blocks.
Divisible by 2
767 ends in 7, so it is odd.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 67 are not divisible by 4.
Divisible by 5
767 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 20 is not a multiple of 9.
Divisible by 10
767 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Deficient classification and digit analytics place 767 within several notable number theory sequences:
Timeline
Deep dive
How 767 breaks down
767 carries 4 distinct factors and a digit signature of 20 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 73, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011111111 supports bitwise reasoning, hexadecimal 2FF aligns with computing notation, and the Roman numeral DCCLXVII keeps the encyclopedic tradition alive. These attributes make 767 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 767 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (762–772) to tune search ranges, and educators feature 767 in worksheets about factor trees. Its binary footprint of length 10 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 767 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 767
Is 767 a prime number?
767 is composite with 4 total factors and the prime factorization 13 × 59.
What is the prime factorization of 767?
It breaks down as 13 × 59, multiplying the primes 13 × 59.
How is 767 represented in binary and hexadecimal?
767 converts to 1011111111 in binary and 2FF in hexadecimal, which are helpful for computer science applications.
Is 767 a perfect square, cube, or triangular number?
767 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 767?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.