968
968 is a even composite number that follows 967 and precedes 969. It is composed of 12 distinct factors: 1, 2, 4, 8, 11, 22, 44, 88, 121, 242, 484, 968. Its prime factorization can be written as 2^3 × 11^2. 968 is classified as a abundant number based on the sum of its proper divisors. In computer science, 968 is represented as 1111001000 in binary and 3C8 in hexadecimal. Historically, it is written as CMLXVIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^3 × 11^2) reveals 5 prime building blocks.
Divisible by 2
968 ends in 8, so it is even.
Divisible by 3
The digit sum 23 is not a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
968 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 23 is not a multiple of 9.
Divisible by 10
968 does not end in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Abundant classification and digit analytics place 968 within several notable number theory sequences:
Timeline
Deep dive
How 968 breaks down
968 carries 12 distinct factors and a digit signature of 23 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 1027, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111001000 supports bitwise reasoning, hexadecimal 3C8 aligns with computing notation, and the Roman numeral CMLXVIII keeps the encyclopedic tradition alive. These attributes make 968 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 968 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (963–973) to tune search ranges, and educators feature 968 in worksheets about factor trees. Its binary footprint of length 10 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 968 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 968
Is 968 a prime number?
968 is composite with 12 total factors and the prime factorization 2^3 × 11^2.
What is the prime factorization of 968?
It breaks down as 2^3 × 11^2, multiplying the primes 2 × 2 × 2 × 11 × 11.
How is 968 represented in binary and hexadecimal?
968 converts to 1111001000 in binary and 3C8 in hexadecimal, which are helpful for computer science applications.
Is 968 a perfect square, cube, or triangular number?
968 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 968?
The digits sum to 23, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.