1216
1216 is a even composite number that follows 1215 and precedes 1217. It is composed of 14 distinct factors: 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 152, 304, 608, 1216. Its prime factorization can be written as 2^6 × 19. 1216 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1216 is represented as 10011000000 in binary and 4C0 in hexadecimal. Historically, it is written as MCCXVI in Roman numerals.
Factor Analysis
14 FactorsProperties
The prime factorization (2^6 × 19) reveals 7 prime building blocks.
Divisible by 2
1216 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
1216 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
1216 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 1216 within several notable number theory sequences:
Timeline
Deep dive
How 1216 breaks down
1216 carries 14 distinct factors and a digit signature of 10 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 1324, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011000000 supports bitwise reasoning, hexadecimal 4C0 aligns with computing notation, and the Roman numeral MCCXVI keeps the encyclopedic tradition alive. These attributes make 1216 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1216 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1211–1221) to tune search ranges, and educators feature 1216 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 1216 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 1216
Is 1216 a prime number?
1216 is composite with 14 total factors and the prime factorization 2^6 × 19.
What is the prime factorization of 1216?
It breaks down as 2^6 × 19, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 19.
How is 1216 represented in binary and hexadecimal?
1216 converts to 10011000000 in binary and 4C0 in hexadecimal, which are helpful for computer science applications.
Is 1216 a perfect square, cube, or triangular number?
1216 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1216?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.