1530
1530 is a even composite number that follows 1529 and precedes 1531. It is composed of 24 distinct factors: 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765, 1530. Its prime factorization can be written as 2 × 3^2 × 5 × 17. 1530 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1530 is represented as 10111111010 in binary and 5FA in hexadecimal. Historically, it is written as MDXXX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2 × 3^2 × 5 × 17) reveals 5 prime building blocks.
Divisible by 2
1530 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 30 are not divisible by 4.
Divisible by 5
1530 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 9 is a multiple of 9.
Divisible by 10
1530 ends in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 1530 within several notable number theory sequences:
Timeline
Deep dive
How 1530 breaks down
1530 carries 24 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 2682, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10111111010 supports bitwise reasoning, hexadecimal 5FA aligns with computing notation, and the Roman numeral MDXXX keeps the encyclopedic tradition alive. These attributes make 1530 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1530 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1525–1535) to tune search ranges, and educators feature 1530 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 1530 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 1530
Is 1530 a prime number?
1530 is composite with 24 total factors and the prime factorization 2 × 3^2 × 5 × 17.
What is the prime factorization of 1530?
It breaks down as 2 × 3^2 × 5 × 17, multiplying the primes 2 × 3 × 3 × 5 × 17.
How is 1530 represented in binary and hexadecimal?
1530 converts to 10111111010 in binary and 5FA in hexadecimal, which are helpful for computer science applications.
Is 1530 a perfect square, cube, or triangular number?
1530 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1530?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.