3872
3872 is a even composite number that follows 3871 and precedes 3873. It is composed of 18 distinct factors: 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 121, 176, 242, 352, 484, 968, 1936, 3872. Its prime factorization can be written as 2^5 × 11^2. 3872 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3872 is represented as 111100100000 in binary and F20 in hexadecimal. Historically, it is written as MMMDCCCLXXII in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^5 × 11^2) reveals 7 prime building blocks.
Divisible by 2
3872 ends in 2, so it is even.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
3872 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 20 is not a multiple of 9.
Divisible by 10
3872 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 3872 within several notable number theory sequences:
Timeline
Deep dive
How 3872 breaks down
3872 carries 18 distinct factors and a digit signature of 20 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 4507, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111100100000 supports bitwise reasoning, hexadecimal F20 aligns with computing notation, and the Roman numeral MMMDCCCLXXII keeps the encyclopedic tradition alive. These attributes make 3872 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3872 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3867–3877) to tune search ranges, and educators feature 3872 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 3872 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 3872
Is 3872 a prime number?
3872 is composite with 18 total factors and the prime factorization 2^5 × 11^2.
What is the prime factorization of 3872?
It breaks down as 2^5 × 11^2, multiplying the primes 2 × 2 × 2 × 2 × 2 × 11 × 11.
How is 3872 represented in binary and hexadecimal?
3872 converts to 111100100000 in binary and F20 in hexadecimal, which are helpful for computer science applications.
Is 3872 a perfect square, cube, or triangular number?
3872 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3872?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.