528
528 is a even composite number that follows 527 and precedes 529. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528. Its prime factorization can be written as 2^4 × 3 × 11. 528 is classified as a abundant number based on the sum of its proper divisors. In computer science, 528 is represented as 1000010000 in binary and 210 in hexadecimal. Historically, it is written as DXXVIII in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 11) reveals 6 prime building blocks.
Divisible by 2
528 ends in 8, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
528 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 15 is not a multiple of 9.
Divisible by 10
528 does not end in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Abundant classification and digit analytics place 528 within several notable number theory sequences:
Timeline
Deep dive
How 528 breaks down
528 carries 20 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 960, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000010000 supports bitwise reasoning, hexadecimal 210 aligns with computing notation, and the Roman numeral DXXVIII keeps the encyclopedic tradition alive. These attributes make 528 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 528 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (523–533) to tune search ranges, and educators feature 528 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, Triangular numbers) help historians, numerologists, and trivia writers tie 528 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 528
Is 528 a prime number?
528 is composite with 20 total factors and the prime factorization 2^4 × 3 × 11.
What is the prime factorization of 528?
It breaks down as 2^4 × 3 × 11, multiplying the primes 2 × 2 × 2 × 2 × 3 × 11.
How is 528 represented in binary and hexadecimal?
528 converts to 1000010000 in binary and 210 in hexadecimal, which are helpful for computer science applications.
Is 528 a perfect square, cube, or triangular number?
528 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 528?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.