3528
3528 is a even composite number that follows 3527 and precedes 3529. It is composed of 36 distinct factors: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 49, 56, 63, 72, 84, 98, 126, 147, 168, 196, 252, 294, 392, 441, 504, 588, 882, 1176, 1764, 3528. Its prime factorization can be written as 2^3 × 3^2 × 7^2. 3528 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3528 is represented as 110111001000 in binary and DC8 in hexadecimal. Historically, it is written as MMMDXXVIII in Roman numerals.
Factor Analysis
36 FactorsProperties
The prime factorization (2^3 × 3^2 × 7^2) reveals 7 prime building blocks.
Divisible by 2
3528 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
3528 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 18 is a multiple of 9.
Divisible by 10
3528 does not end in 0.
Divisible by 11
The alternating digit sum -8 is not a multiple of 11.
Abundant classification and digit analytics place 3528 within several notable number theory sequences:
Timeline
Deep dive
How 3528 breaks down
3528 carries 36 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 7587, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110111001000 supports bitwise reasoning, hexadecimal DC8 aligns with computing notation, and the Roman numeral MMMDXXVIII keeps the encyclopedic tradition alive. These attributes make 3528 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3528 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3523–3533) to tune search ranges, and educators feature 3528 in worksheets about factor trees. Its binary footprint of length 12 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 3528 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 3528
Is 3528 a prime number?
3528 is composite with 36 total factors and the prime factorization 2^3 × 3^2 × 7^2.
What is the prime factorization of 3528?
It breaks down as 2^3 × 3^2 × 7^2, multiplying the primes 2 × 2 × 2 × 3 × 3 × 7 × 7.
How is 3528 represented in binary and hexadecimal?
3528 converts to 110111001000 in binary and DC8 in hexadecimal, which are helpful for computer science applications.
Is 3528 a perfect square, cube, or triangular number?
3528 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3528?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.