2210
2210 is a even composite number that follows 2209 and precedes 2211. It is composed of 16 distinct factors: 1, 2, 5, 10, 13, 17, 26, 34, 65, 85, 130, 170, 221, 442, 1105, 2210. Its prime factorization can be written as 2 × 5 × 13 × 17. 2210 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2210 is represented as 100010100010 in binary and 8A2 in hexadecimal. Historically, it is written as MMCCX in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 5 × 13 × 17) reveals 4 prime building blocks.
Divisible by 2
2210 ends in 0, so it is even.
Divisible by 3
The digit sum 5 is not a multiple of 3.
Divisible by 4
The last two digits 10 are not divisible by 4.
Divisible by 5
2210 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 5 is not a multiple of 9.
Divisible by 10
2210 ends in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 2210 within several notable number theory sequences:
Timeline
Deep dive
How 2210 breaks down
2210 carries 16 distinct factors and a digit signature of 5 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 2326, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100010100010 supports bitwise reasoning, hexadecimal 8A2 aligns with computing notation, and the Roman numeral MMCCX keeps the encyclopedic tradition alive. These attributes make 2210 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2210 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2205–2215) to tune search ranges, and educators feature 2210 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, Abundant numbers) help historians, numerologists, and trivia writers tie 2210 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 2210
Is 2210 a prime number?
2210 is composite with 16 total factors and the prime factorization 2 × 5 × 13 × 17.
What is the prime factorization of 2210?
It breaks down as 2 × 5 × 13 × 17, multiplying the primes 2 × 5 × 13 × 17.
How is 2210 represented in binary and hexadecimal?
2210 converts to 100010100010 in binary and 8A2 in hexadecimal, which are helpful for computer science applications.
Is 2210 a perfect square, cube, or triangular number?
2210 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2210?
The digits sum to 5, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.