3964
3964 is a even composite number that follows 3963 and precedes 3965. It is composed of 6 distinct factors: 1, 2, 4, 991, 1982, 3964. Its prime factorization can be written as 2^2 × 991. 3964 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3964 is represented as 111101111100 in binary and F7C in hexadecimal. Historically, it is written as MMMCMLXIV in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (2^2 × 991) reveals 3 prime building blocks.
Divisible by 2
3964 ends in 4, so it is even.
Divisible by 3
The digit sum 22 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
3964 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 22 is not a multiple of 9.
Divisible by 10
3964 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Deficient classification and digit analytics place 3964 within several notable number theory sequences:
Timeline
Deep dive
How 3964 breaks down
3964 carries 6 distinct factors and a digit signature of 22 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 2980, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111101111100 supports bitwise reasoning, hexadecimal F7C aligns with computing notation, and the Roman numeral MMMCMLXIV keeps the encyclopedic tradition alive. These attributes make 3964 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3964 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3959–3969) to tune search ranges, and educators feature 3964 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, Deficient numbers) help historians, numerologists, and trivia writers tie 3964 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 3964
Is 3964 a prime number?
3964 is composite with 6 total factors and the prime factorization 2^2 × 991.
What is the prime factorization of 3964?
It breaks down as 2^2 × 991, multiplying the primes 2 × 2 × 991.
How is 3964 represented in binary and hexadecimal?
3964 converts to 111101111100 in binary and F7C in hexadecimal, which are helpful for computer science applications.
Is 3964 a perfect square, cube, or triangular number?
3964 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3964?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.