168
168 is a even composite number that follows 167 and precedes 169. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. Its prime factorization can be written as 2^3 × 3 × 7. 168 is classified as a abundant number based on the sum of its proper divisors. In computer science, 168 is represented as 10101000 in binary and A8 in hexadecimal. Historically, it is written as CLXVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 7) reveals 5 prime building blocks.
Divisible by 2
168 ends in 8, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
168 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 15 is not a multiple of 9.
Divisible by 10
168 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 168 within several notable number theory sequences:
Timeline
Deep dive
How 168 breaks down
168 carries 16 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 312, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10101000 supports bitwise reasoning, hexadecimal A8 aligns with computing notation, and the Roman numeral CLXVIII keeps the encyclopedic tradition alive. These attributes make 168 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 168 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (163–173) to tune search ranges, and educators feature 168 in worksheets about factor trees. Its binary footprint of length 8 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 168 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 168
Is 168 a prime number?
168 is composite with 16 total factors and the prime factorization 2^3 × 3 × 7.
What is the prime factorization of 168?
It breaks down as 2^3 × 3 × 7, multiplying the primes 2 × 2 × 2 × 3 × 7.
How is 168 represented in binary and hexadecimal?
168 converts to 10101000 in binary and A8 in hexadecimal, which are helpful for computer science applications.
Is 168 a perfect square, cube, or triangular number?
168 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 168?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.