4212
4212 is a even composite number that follows 4211 and precedes 4213. It is composed of 30 distinct factors: 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 81, 108, 117, 156, 162, 234, 324, 351, 468, 702, 1053, 1404, 2106, 4212. Its prime factorization can be written as 2^2 × 3^4 × 13. 4212 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4212 is represented as 1000001110100 in binary and 1074 in hexadecimal.
Factor Analysis
30 FactorsProperties
The prime factorization (2^2 × 3^4 × 13) reveals 7 prime building blocks.
Divisible by 2
4212 ends in 2, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 12 form a multiple of 4.
Divisible by 5
4212 does not end in 0 or 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 9 is a multiple of 9.
Divisible by 10
4212 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 4212 within several notable number theory sequences:
Timeline
Deep dive
How 4212 breaks down
4212 carries 30 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 7646, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000001110100 supports bitwise reasoning, hexadecimal 1074 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4212 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4212 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4207–4217) to tune search ranges, and educators feature 4212 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 4212 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 4212
Is 4212 a prime number?
4212 is composite with 30 total factors and the prime factorization 2^2 × 3^4 × 13.
What is the prime factorization of 4212?
It breaks down as 2^2 × 3^4 × 13, multiplying the primes 2 × 2 × 3 × 3 × 3 × 3 × 13.
How is 4212 represented in binary and hexadecimal?
4212 converts to 1000001110100 in binary and 1074 in hexadecimal, which are helpful for computer science applications.
Is 4212 a perfect square, cube, or triangular number?
4212 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4212?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.