2220
2220 is a even composite number that follows 2219 and precedes 2221. It is composed of 24 distinct factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 37, 60, 74, 111, 148, 185, 222, 370, 444, 555, 740, 1110, 2220. Its prime factorization can be written as 2^2 × 3 × 5 × 37. 2220 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2220 is represented as 100010101100 in binary and 8AC in hexadecimal. Historically, it is written as MMCCXX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 5 × 37) reveals 5 prime building blocks.
Divisible by 2
2220 ends in 0, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
2220 ends in 0, so it is divisible by 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 6 is not a multiple of 9.
Divisible by 10
2220 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 2220 within several notable number theory sequences:
Timeline
Deep dive
How 2220 breaks down
2220 carries 24 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 4164, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100010101100 supports bitwise reasoning, hexadecimal 8AC aligns with computing notation, and the Roman numeral MMCCXX keeps the encyclopedic tradition alive. These attributes make 2220 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2220 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2215–2225) to tune search ranges, and educators feature 2220 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 2220 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 2220
Is 2220 a prime number?
2220 is composite with 24 total factors and the prime factorization 2^2 × 3 × 5 × 37.
What is the prime factorization of 2220?
It breaks down as 2^2 × 3 × 5 × 37, multiplying the primes 2 × 2 × 3 × 5 × 37.
How is 2220 represented in binary and hexadecimal?
2220 converts to 100010101100 in binary and 8AC in hexadecimal, which are helpful for computer science applications.
Is 2220 a perfect square, cube, or triangular number?
2220 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2220?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.