27200
27200 is a even composite number that follows 27199 and precedes 27201. It is composed of 42 distinct factors: 1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 64, 68, 80, 85, 100, 136, 160, 170, 200, 272, 320, 340, 400, 425, 544, 680, 800, 850, 1088, 1360, 1600, 1700, 2720, 3400, 5440, 6800, 13600, 27200. Its prime factorization can be written as 2^6 × 5^2 × 17. 27200 is classified as a abundant number based on the sum of its proper divisors. In computer science, 27200 is represented as 110101001000000 in binary and 6A40 in hexadecimal.
Factor Analysis
42 FactorsProperties
The prime factorization (2^6 × 5^2 × 17) reveals 9 prime building blocks.
Divisible by 2
27200 ends in 0, so it is even.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
27200 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 11 is not a multiple of 9.
Divisible by 10
27200 ends in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 27200 within several notable number theory sequences:
Timeline
Deep dive
How 27200 breaks down
27200 carries 42 distinct factors and a digit signature of 11 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 43666, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110101001000000 supports bitwise reasoning, hexadecimal 6A40 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 27200 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 27200 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (27195–27205) to tune search ranges, and educators feature 27200 in worksheets about factor trees. Its binary footprint of length 15 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 27200 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 27200
Is 27200 a prime number?
27200 is composite with 42 total factors and the prime factorization 2^6 × 5^2 × 17.
What is the prime factorization of 27200?
It breaks down as 2^6 × 5^2 × 17, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 17.
How is 27200 represented in binary and hexadecimal?
27200 converts to 110101001000000 in binary and 6A40 in hexadecimal, which are helpful for computer science applications.
Is 27200 a perfect square, cube, or triangular number?
27200 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 27200?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.