8520
8520 is a even composite number that follows 8519 and precedes 8521. It is composed of 32 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 71, 120, 142, 213, 284, 355, 426, 568, 710, 852, 1065, 1420, 1704, 2130, 2840, 4260, 8520. Its prime factorization can be written as 2^3 × 3 × 5 × 71. 8520 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8520 is represented as 10000101001000 in binary and 2148 in hexadecimal.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 3 × 5 × 71) reveals 6 prime building blocks.
Divisible by 2
8520 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 20 form a multiple of 4.
Divisible by 5
8520 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
8520 ends in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 8520 within several notable number theory sequences:
Timeline
Deep dive
How 8520 breaks down
8520 carries 32 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 17400, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000101001000 supports bitwise reasoning, hexadecimal 2148 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8520 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8520 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8515–8525) to tune search ranges, and educators feature 8520 in worksheets about factor trees. Its binary footprint of length 14 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 8520 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 8520
Is 8520 a prime number?
8520 is composite with 32 total factors and the prime factorization 2^3 × 3 × 5 × 71.
What is the prime factorization of 8520?
It breaks down as 2^3 × 3 × 5 × 71, multiplying the primes 2 × 2 × 2 × 3 × 5 × 71.
How is 8520 represented in binary and hexadecimal?
8520 converts to 10000101001000 in binary and 2148 in hexadecimal, which are helpful for computer science applications.
Is 8520 a perfect square, cube, or triangular number?
8520 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8520?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.