588
588 is a even composite number that follows 587 and precedes 589. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588. Its prime factorization can be written as 2^2 × 3 × 7^2. 588 is classified as a abundant number based on the sum of its proper divisors. In computer science, 588 is represented as 1001001100 in binary and 24C in hexadecimal. Historically, it is written as DLXXXVIII in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 3 × 7^2) reveals 5 prime building blocks.
Divisible by 2
588 ends in 8, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 88 form a multiple of 4.
Divisible by 5
588 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 21 is not a multiple of 9.
Divisible by 10
588 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 588 within several notable number theory sequences:
Timeline
Deep dive
How 588 breaks down
588 carries 18 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 1008, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001001100 supports bitwise reasoning, hexadecimal 24C aligns with computing notation, and the Roman numeral DLXXXVIII keeps the encyclopedic tradition alive. These attributes make 588 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 588 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (583–593) to tune search ranges, and educators feature 588 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 588 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 588
Is 588 a prime number?
588 is composite with 18 total factors and the prime factorization 2^2 × 3 × 7^2.
What is the prime factorization of 588?
It breaks down as 2^2 × 3 × 7^2, multiplying the primes 2 × 2 × 3 × 7 × 7.
How is 588 represented in binary and hexadecimal?
588 converts to 1001001100 in binary and 24C in hexadecimal, which are helpful for computer science applications.
Is 588 a perfect square, cube, or triangular number?
588 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 588?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.