3936
3936 is a even composite number that follows 3935 and precedes 3937. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 41, 48, 82, 96, 123, 164, 246, 328, 492, 656, 984, 1312, 1968, 3936. Its prime factorization can be written as 2^5 × 3 × 41. 3936 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3936 is represented as 111101100000 in binary and F60 in hexadecimal. Historically, it is written as MMMCMXXXVI in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^5 × 3 × 41) reveals 7 prime building blocks.
Divisible by 2
3936 ends in 6, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 36 form a multiple of 4.
Divisible by 5
3936 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 21 is not a multiple of 9.
Divisible by 10
3936 does not end in 0.
Divisible by 11
The alternating digit sum -9 is not a multiple of 11.
Abundant classification and digit analytics place 3936 within several notable number theory sequences:
Timeline
Deep dive
How 3936 breaks down
3936 carries 24 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 6648, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111101100000 supports bitwise reasoning, hexadecimal F60 aligns with computing notation, and the Roman numeral MMMCMXXXVI keeps the encyclopedic tradition alive. These attributes make 3936 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3936 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3931–3941) to tune search ranges, and educators feature 3936 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 3936 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 3936
Is 3936 a prime number?
3936 is composite with 24 total factors and the prime factorization 2^5 × 3 × 41.
What is the prime factorization of 3936?
It breaks down as 2^5 × 3 × 41, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 41.
How is 3936 represented in binary and hexadecimal?
3936 converts to 111101100000 in binary and F60 in hexadecimal, which are helpful for computer science applications.
Is 3936 a perfect square, cube, or triangular number?
3936 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3936?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.