2016
2016 is a even composite number that follows 2015 and precedes 2017. It is composed of 36 distinct factors: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016. Its prime factorization can be written as 2^5 × 3^2 × 7. 2016 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2016 is represented as 11111100000 in binary and 7E0 in hexadecimal. Historically, it is written as MMXVI in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
36 FactorsProperties
The prime factorization (2^5 × 3^2 × 7) reveals 8 prime building blocks.
Divisible by 2
2016 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
2016 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
2016 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 2016 within several notable number theory sequences:
Timeline
Deep dive
How 2016 breaks down
2016 carries 36 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 4536, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11111100000 supports bitwise reasoning, hexadecimal 7E0 aligns with computing notation, and the Roman numeral MMXVI keeps the encyclopedic tradition alive. These attributes make 2016 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2016 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2011–2021) to tune search ranges, and educators feature 2016 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, Triangular numbers) help historians, numerologists, and trivia writers tie 2016 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 2016
Is 2016 a prime number?
2016 is composite with 36 total factors and the prime factorization 2^5 × 3^2 × 7.
What is the prime factorization of 2016?
It breaks down as 2^5 × 3^2 × 7, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7.
How is 2016 represented in binary and hexadecimal?
2016 converts to 11111100000 in binary and 7E0 in hexadecimal, which are helpful for computer science applications.
Is 2016 a perfect square, cube, or triangular number?
2016 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 2016?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.