1116
1116 is a even composite number that follows 1115 and precedes 1117. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116. Its prime factorization can be written as 2^2 × 3^2 × 31. 1116 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1116 is represented as 10001011100 in binary and 45C in hexadecimal. Historically, it is written as MCXVI in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 3^2 × 31) reveals 5 prime building blocks.
Divisible by 2
1116 ends in 6, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 16 form a multiple of 4.
Divisible by 5
1116 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 9 is a multiple of 9.
Divisible by 10
1116 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Abundant classification and digit analytics place 1116 within several notable number theory sequences:
Timeline
Deep dive
How 1116 breaks down
1116 carries 18 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1796, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10001011100 supports bitwise reasoning, hexadecimal 45C aligns with computing notation, and the Roman numeral MCXVI keeps the encyclopedic tradition alive. These attributes make 1116 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1116 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1111–1121) to tune search ranges, and educators feature 1116 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 1116 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 1116
Is 1116 a prime number?
1116 is composite with 18 total factors and the prime factorization 2^2 × 3^2 × 31.
What is the prime factorization of 1116?
It breaks down as 2^2 × 3^2 × 31, multiplying the primes 2 × 2 × 3 × 3 × 31.
How is 1116 represented in binary and hexadecimal?
1116 converts to 10001011100 in binary and 45C in hexadecimal, which are helpful for computer science applications.
Is 1116 a perfect square, cube, or triangular number?
1116 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1116?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.