5200
5200 is a even composite number that follows 5199 and precedes 5201. It is composed of 30 distinct factors: 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200. Its prime factorization can be written as 2^4 × 5^2 × 13. 5200 is classified as a abundant number based on the sum of its proper divisors. In computer science, 5200 is represented as 1010001010000 in binary and 1450 in hexadecimal.
Factor Analysis
30 FactorsProperties
The prime factorization (2^4 × 5^2 × 13) reveals 7 prime building blocks.
Divisible by 2
5200 ends in 0, so it is even.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
5200 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 7 is not a multiple of 9.
Divisible by 10
5200 ends in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 5200 within several notable number theory sequences:
Timeline
Deep dive
How 5200 breaks down
5200 carries 30 distinct factors and a digit signature of 7 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 8254, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010001010000 supports bitwise reasoning, hexadecimal 1450 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 5200 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 5200 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (5195–5205) to tune search ranges, and educators feature 5200 in worksheets about factor trees. Its binary footprint of length 13 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 5200 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 5200
Is 5200 a prime number?
5200 is composite with 30 total factors and the prime factorization 2^4 × 5^2 × 13.
What is the prime factorization of 5200?
It breaks down as 2^4 × 5^2 × 13, multiplying the primes 2 × 2 × 2 × 2 × 5 × 5 × 13.
How is 5200 represented in binary and hexadecimal?
5200 converts to 1010001010000 in binary and 1450 in hexadecimal, which are helpful for computer science applications.
Is 5200 a perfect square, cube, or triangular number?
5200 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 5200?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.