1788
1788 is a even composite number that follows 1787 and precedes 1789. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 12, 149, 298, 447, 596, 894, 1788. Its prime factorization can be written as 2^2 × 3 × 149. 1788 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1788 is represented as 11011111100 in binary and 6FC in hexadecimal. Historically, it is written as MDCCLXXXVIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3 × 149) reveals 4 prime building blocks.
Divisible by 2
1788 ends in 8, so it is even.
Divisible by 3
The digit sum 24 is a multiple of 3.
Divisible by 4
The last two digits 88 form a multiple of 4.
Divisible by 5
1788 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 24 is not a multiple of 9.
Divisible by 10
1788 does not end in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Abundant classification and digit analytics place 1788 within several notable number theory sequences:
Timeline
Deep dive
How 1788 breaks down
1788 carries 12 distinct factors and a digit signature of 24 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2412, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011111100 supports bitwise reasoning, hexadecimal 6FC aligns with computing notation, and the Roman numeral MDCCLXXXVIII keeps the encyclopedic tradition alive. These attributes make 1788 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1788 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1783–1793) to tune search ranges, and educators feature 1788 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 1788 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 1788
Is 1788 a prime number?
1788 is composite with 12 total factors and the prime factorization 2^2 × 3 × 149.
What is the prime factorization of 1788?
It breaks down as 2^2 × 3 × 149, multiplying the primes 2 × 2 × 3 × 149.
How is 1788 represented in binary and hexadecimal?
1788 converts to 11011111100 in binary and 6FC in hexadecimal, which are helpful for computer science applications.
Is 1788 a perfect square, cube, or triangular number?
1788 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1788?
The digits sum to 24, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.