3822
3822 is a even composite number that follows 3821 and precedes 3823. It is composed of 24 distinct factors: 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 49, 78, 91, 98, 147, 182, 273, 294, 546, 637, 1274, 1911, 3822. Its prime factorization can be written as 2 × 3 × 7^2 × 13. 3822 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3822 is represented as 111011101110 in binary and EEE in hexadecimal. Historically, it is written as MMMDCCCXXII in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2 × 3 × 7^2 × 13) reveals 5 prime building blocks.
Divisible by 2
3822 ends in 2, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 22 are not divisible by 4.
Divisible by 5
3822 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 15 is not a multiple of 9.
Divisible by 10
3822 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Abundant classification and digit analytics place 3822 within several notable number theory sequences:
Timeline
Deep dive
How 3822 breaks down
3822 carries 24 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 5754, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111011101110 supports bitwise reasoning, hexadecimal EEE aligns with computing notation, and the Roman numeral MMMDCCCXXII keeps the encyclopedic tradition alive. These attributes make 3822 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3822 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3817–3827) to tune search ranges, and educators feature 3822 in worksheets about factor trees. Its binary footprint of length 12 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 3822 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 3822
Is 3822 a prime number?
3822 is composite with 24 total factors and the prime factorization 2 × 3 × 7^2 × 13.
What is the prime factorization of 3822?
It breaks down as 2 × 3 × 7^2 × 13, multiplying the primes 2 × 3 × 7 × 7 × 13.
How is 3822 represented in binary and hexadecimal?
3822 converts to 111011101110 in binary and EEE in hexadecimal, which are helpful for computer science applications.
Is 3822 a perfect square, cube, or triangular number?
3822 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3822?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.