1590
1590 is a even composite number that follows 1589 and precedes 1591. It is composed of 16 distinct factors: 1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795, 1590. Its prime factorization can be written as 2 × 3 × 5 × 53. 1590 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1590 is represented as 11000110110 in binary and 636 in hexadecimal. Historically, it is written as MDXC in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3 × 5 × 53) reveals 4 prime building blocks.
Divisible by 2
1590 ends in 0, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 90 are not divisible by 4.
Divisible by 5
1590 ends in 0, so it is divisible by 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
1590 ends in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 1590 within several notable number theory sequences:
Timeline
Deep dive
How 1590 breaks down
1590 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 2298, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11000110110 supports bitwise reasoning, hexadecimal 636 aligns with computing notation, and the Roman numeral MDXC keeps the encyclopedic tradition alive. These attributes make 1590 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1590 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1585–1595) to tune search ranges, and educators feature 1590 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, Abundant numbers) help historians, numerologists, and trivia writers tie 1590 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 1590
Is 1590 a prime number?
1590 is composite with 16 total factors and the prime factorization 2 × 3 × 5 × 53.
What is the prime factorization of 1590?
It breaks down as 2 × 3 × 5 × 53, multiplying the primes 2 × 3 × 5 × 53.
How is 1590 represented in binary and hexadecimal?
1590 converts to 11000110110 in binary and 636 in hexadecimal, which are helpful for computer science applications.
Is 1590 a perfect square, cube, or triangular number?
1590 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1590?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.