7968
7968 is a even composite number that follows 7967 and precedes 7969. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 83, 96, 166, 249, 332, 498, 664, 996, 1328, 1992, 2656, 3984, 7968. Its prime factorization can be written as 2^5 × 3 × 83. 7968 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7968 is represented as 1111100100000 in binary and 1F20 in hexadecimal.
Factor Analysis
24 FactorsProperties
The prime factorization (2^5 × 3 × 83) reveals 7 prime building blocks.
Divisible by 2
7968 ends in 8, so it is even.
Divisible by 3
The digit sum 30 is a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
7968 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 30 is not a multiple of 9.
Divisible by 10
7968 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 7968 within several notable number theory sequences:
Timeline
Deep dive
How 7968 breaks down
7968 carries 24 distinct factors and a digit signature of 30 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 13200, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111100100000 supports bitwise reasoning, hexadecimal 1F20 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7968 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7968 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7963–7973) to tune search ranges, and educators feature 7968 in worksheets about factor trees. Its binary footprint of length 13 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 7968 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 7968
Is 7968 a prime number?
7968 is composite with 24 total factors and the prime factorization 2^5 × 3 × 83.
What is the prime factorization of 7968?
It breaks down as 2^5 × 3 × 83, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 83.
How is 7968 represented in binary and hexadecimal?
7968 converts to 1111100100000 in binary and 1F20 in hexadecimal, which are helpful for computer science applications.
Is 7968 a perfect square, cube, or triangular number?
7968 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7968?
The digits sum to 30, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.