108
108 is a even composite number that follows 107 and precedes 109. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. Its prime factorization can be written as 2^2 × 3^3. 108 is classified as a abundant number based on the sum of its proper divisors. In computer science, 108 is represented as 1101100 in binary and 6C in hexadecimal. Historically, it is written as CVIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3^3) reveals 5 prime building blocks.
Divisible by 2
108 ends in 8, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
108 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 9 is a multiple of 9.
Divisible by 10
108 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 108 within several notable number theory sequences:
Timeline
Deep dive
How 108 breaks down
108 carries 12 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 172, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101100 supports bitwise reasoning, hexadecimal 6C aligns with computing notation, and the Roman numeral CVIII keeps the encyclopedic tradition alive. These attributes make 108 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 108 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (103–113) to tune search ranges, and educators feature 108 in worksheets about factor trees. Its binary footprint of length 7 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 108 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 108
Is 108 a prime number?
108 is composite with 12 total factors and the prime factorization 2^2 × 3^3.
What is the prime factorization of 108?
It breaks down as 2^2 × 3^3, multiplying the primes 2 × 2 × 3 × 3 × 3.
How is 108 represented in binary and hexadecimal?
108 converts to 1101100 in binary and 6C in hexadecimal, which are helpful for computer science applications.
Is 108 a perfect square, cube, or triangular number?
108 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 108?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.