4200
4200 is a even composite number that follows 4199 and precedes 4201. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200. Its prime factorization can be written as 2^3 × 3 × 5^2 × 7. 4200 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4200 is represented as 1000001101000 in binary and 1068 in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^3 × 3 × 5^2 × 7) reveals 7 prime building blocks.
Divisible by 2
4200 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 00 form a multiple of 4.
Divisible by 5
4200 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
4200 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 4200 within several notable number theory sequences:
Timeline
Deep dive
How 4200 breaks down
4200 carries 48 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 10680, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000001101000 supports bitwise reasoning, hexadecimal 1068 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4200 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4200 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4195–4205) to tune search ranges, and educators feature 4200 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 4200 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 4200
Is 4200 a prime number?
4200 is composite with 48 total factors and the prime factorization 2^3 × 3 × 5^2 × 7.
What is the prime factorization of 4200?
It breaks down as 2^3 × 3 × 5^2 × 7, multiplying the primes 2 × 2 × 2 × 3 × 5 × 5 × 7.
How is 4200 represented in binary and hexadecimal?
4200 converts to 1000001101000 in binary and 1068 in hexadecimal, which are helpful for computer science applications.
Is 4200 a perfect square, cube, or triangular number?
4200 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4200?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.