3968
3968 is a even composite number that follows 3967 and precedes 3969. It is composed of 16 distinct factors: 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 128, 248, 496, 992, 1984, 3968. Its prime factorization can be written as 2^7 × 31. 3968 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3968 is represented as 111110000000 in binary and F80 in hexadecimal. Historically, it is written as MMMCMLXVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^7 × 31) reveals 8 prime building blocks.
Divisible by 2
3968 ends in 8, so it is even.
Divisible by 3
The digit sum 26 is not a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
3968 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 26 is not a multiple of 9.
Divisible by 10
3968 does not end in 0.
Divisible by 11
The alternating digit sum -8 is not a multiple of 11.
Abundant classification and digit analytics place 3968 within several notable number theory sequences:
Timeline
Deep dive
How 3968 breaks down
3968 carries 16 distinct factors and a digit signature of 26 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 4192, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111110000000 supports bitwise reasoning, hexadecimal F80 aligns with computing notation, and the Roman numeral MMMCMLXVIII keeps the encyclopedic tradition alive. These attributes make 3968 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3968 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3963–3973) to tune search ranges, and educators feature 3968 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 3968 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 3968
Is 3968 a prime number?
3968 is composite with 16 total factors and the prime factorization 2^7 × 31.
What is the prime factorization of 3968?
It breaks down as 2^7 × 31, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 31.
How is 3968 represented in binary and hexadecimal?
3968 converts to 111110000000 in binary and F80 in hexadecimal, which are helpful for computer science applications.
Is 3968 a perfect square, cube, or triangular number?
3968 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3968?
The digits sum to 26, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.