2520
2520 is a even composite number that follows 2519 and precedes 2521. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520. Its prime factorization can be written as 2^3 × 3^2 × 5 × 7. 2520 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2520 is represented as 100111011000 in binary and 9D8 in hexadecimal. Historically, it is written as MMDXX in Roman numerals.
Factor Analysis
48 FactorsProperties
The prime factorization (2^3 × 3^2 × 5 × 7) reveals 7 prime building blocks.
Divisible by 2
2520 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 20 form a multiple of 4.
Divisible by 5
2520 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
2520 ends in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 2520 within several notable number theory sequences:
Timeline
Deep dive
How 2520 breaks down
2520 carries 48 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 6840, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100111011000 supports bitwise reasoning, hexadecimal 9D8 aligns with computing notation, and the Roman numeral MMDXX keeps the encyclopedic tradition alive. These attributes make 2520 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2520 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2515–2525) to tune search ranges, and educators feature 2520 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 2520 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 2520
Is 2520 a prime number?
2520 is composite with 48 total factors and the prime factorization 2^3 × 3^2 × 5 × 7.
What is the prime factorization of 2520?
It breaks down as 2^3 × 3^2 × 5 × 7, multiplying the primes 2 × 2 × 2 × 3 × 3 × 5 × 7.
How is 2520 represented in binary and hexadecimal?
2520 converts to 100111011000 in binary and 9D8 in hexadecimal, which are helpful for computer science applications.
Is 2520 a perfect square, cube, or triangular number?
2520 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2520?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.