7208
7208 is a even composite number that follows 7207 and precedes 7209. It is composed of 16 distinct factors: 1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604, 7208. Its prime factorization can be written as 2^3 × 17 × 53. 7208 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7208 is represented as 1110000101000 in binary and 1C28 in hexadecimal.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 17 × 53) reveals 5 prime building blocks.
Divisible by 2
7208 ends in 8, so it is even.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
7208 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 17 is not a multiple of 9.
Divisible by 10
7208 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 7208 within several notable number theory sequences:
Timeline
Deep dive
How 7208 breaks down
7208 carries 16 distinct factors and a digit signature of 17 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 7372, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1110000101000 supports bitwise reasoning, hexadecimal 1C28 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7208 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7208 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7203–7213) to tune search ranges, and educators feature 7208 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 7208 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 7208
Is 7208 a prime number?
7208 is composite with 16 total factors and the prime factorization 2^3 × 17 × 53.
What is the prime factorization of 7208?
It breaks down as 2^3 × 17 × 53, multiplying the primes 2 × 2 × 2 × 17 × 53.
How is 7208 represented in binary and hexadecimal?
7208 converts to 1110000101000 in binary and 1C28 in hexadecimal, which are helpful for computer science applications.
Is 7208 a perfect square, cube, or triangular number?
7208 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7208?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.