1588
1588 is a even composite number that follows 1587 and precedes 1589. It is composed of 6 distinct factors: 1, 2, 4, 397, 794, 1588. Its prime factorization can be written as 2^2 × 397. 1588 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1588 is represented as 11000110100 in binary and 634 in hexadecimal. Historically, it is written as MDLXXXVIII in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (2^2 × 397) reveals 3 prime building blocks.
Divisible by 2
1588 ends in 8, so it is even.
Divisible by 3
The digit sum 22 is not a multiple of 3.
Divisible by 4
The last two digits 88 form a multiple of 4.
Divisible by 5
1588 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 22 is not a multiple of 9.
Divisible by 10
1588 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Deficient classification and digit analytics place 1588 within several notable number theory sequences:
Timeline
Deep dive
How 1588 breaks down
1588 carries 6 distinct factors and a digit signature of 22 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 1198, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11000110100 supports bitwise reasoning, hexadecimal 634 aligns with computing notation, and the Roman numeral MDLXXXVIII keeps the encyclopedic tradition alive. These attributes make 1588 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1588 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1583–1593) to tune search ranges, and educators feature 1588 in worksheets about factor trees. Its binary footprint of length 11 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 1588 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 1588
Is 1588 a prime number?
1588 is composite with 6 total factors and the prime factorization 2^2 × 397.
What is the prime factorization of 1588?
It breaks down as 2^2 × 397, multiplying the primes 2 × 2 × 397.
How is 1588 represented in binary and hexadecimal?
1588 converts to 11000110100 in binary and 634 in hexadecimal, which are helpful for computer science applications.
Is 1588 a perfect square, cube, or triangular number?
1588 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1588?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.