288
288 is a even composite number that follows 287 and precedes 289. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288. Its prime factorization can be written as 2^5 × 3^2. 288 is classified as a abundant number based on the sum of its proper divisors. In computer science, 288 is represented as 100100000 in binary and 120 in hexadecimal. Historically, it is written as CCLXXXVIII in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^5 × 3^2) reveals 7 prime building blocks.
Divisible by 2
288 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 88 form a multiple of 4.
Divisible by 5
288 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 18 is a multiple of 9.
Divisible by 10
288 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 288 within several notable number theory sequences:
Timeline
Deep dive
How 288 breaks down
288 carries 18 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 531, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100100000 supports bitwise reasoning, hexadecimal 120 aligns with computing notation, and the Roman numeral CCLXXXVIII keeps the encyclopedic tradition alive. These attributes make 288 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 288 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (283–293) to tune search ranges, and educators feature 288 in worksheets about factor trees. Its binary footprint of length 9 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 288 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 288
Is 288 a prime number?
288 is composite with 18 total factors and the prime factorization 2^5 × 3^2.
What is the prime factorization of 288?
It breaks down as 2^5 × 3^2, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 3.
How is 288 represented in binary and hexadecimal?
288 converts to 100100000 in binary and 120 in hexadecimal, which are helpful for computer science applications.
Is 288 a perfect square, cube, or triangular number?
288 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 288?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.