2116
2116 is a even composite number that follows 2115 and precedes 2117. It is composed of 9 distinct factors: 1, 2, 4, 23, 46, 92, 529, 1058, 2116. Its prime factorization can be written as 2^2 × 23^2. 2116 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2116 is represented as 100001000100 in binary and 844 in hexadecimal. Historically, it is written as MMCXVI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
9 FactorsProperties
The prime factorization (2^2 × 23^2) reveals 4 prime building blocks.
Divisible by 2
2116 ends in 6, so it is even.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 16 form a multiple of 4.
Divisible by 5
2116 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 10 is not a multiple of 9.
Divisible by 10
2116 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Deficient classification and digit analytics place 2116 within several notable number theory sequences:
Timeline
Deep dive
How 2116 breaks down
2116 carries 9 distinct factors and a digit signature of 10 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 1755, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100001000100 supports bitwise reasoning, hexadecimal 844 aligns with computing notation, and the Roman numeral MMCXVI keeps the encyclopedic tradition alive. These attributes make 2116 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2116 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2111–2121) to tune search ranges, and educators feature 2116 in worksheets about factor trees. Its binary footprint of length 12 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers, Perfect squares) help historians, numerologists, and trivia writers tie 2116 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 2116
Is 2116 a prime number?
2116 is composite with 9 total factors and the prime factorization 2^2 × 23^2.
What is the prime factorization of 2116?
It breaks down as 2^2 × 23^2, multiplying the primes 2 × 2 × 23 × 23.
How is 2116 represented in binary and hexadecimal?
2116 converts to 100001000100 in binary and 844 in hexadecimal, which are helpful for computer science applications.
Is 2116 a perfect square, cube, or triangular number?
2116 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2116?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.