4208
4208 is a even composite number that follows 4207 and precedes 4209. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 263, 526, 1052, 2104, 4208. Its prime factorization can be written as 2^4 × 263. 4208 is classified as a deficient number based on the sum of its proper divisors. In computer science, 4208 is represented as 1000001110000 in binary and 1070 in hexadecimal.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 263) reveals 5 prime building blocks.
Divisible by 2
4208 ends in 8, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
4208 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 14 is not a multiple of 9.
Divisible by 10
4208 does not end in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Deficient classification and digit analytics place 4208 within several notable number theory sequences:
Timeline
Deep dive
How 4208 breaks down
4208 carries 10 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 3976, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000001110000 supports bitwise reasoning, hexadecimal 1070 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4208 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4208 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4203–4213) to tune search ranges, and educators feature 4208 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, Deficient numbers) help historians, numerologists, and trivia writers tie 4208 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 4208
Is 4208 a prime number?
4208 is composite with 10 total factors and the prime factorization 2^4 × 263.
What is the prime factorization of 4208?
It breaks down as 2^4 × 263, multiplying the primes 2 × 2 × 2 × 2 × 263.
How is 4208 represented in binary and hexadecimal?
4208 converts to 1000001110000 in binary and 1070 in hexadecimal, which are helpful for computer science applications.
Is 4208 a perfect square, cube, or triangular number?
4208 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4208?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.