1520
1520 is a even composite number that follows 1519 and precedes 1521. It is composed of 20 distinct factors: 1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760, 1520. Its prime factorization can be written as 2^4 × 5 × 19. 1520 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1520 is represented as 10111110000 in binary and 5F0 in hexadecimal. Historically, it is written as MDXX in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 5 × 19) reveals 6 prime building blocks.
Divisible by 2
1520 ends in 0, so it is even.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
1520 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 8 is not a multiple of 9.
Divisible by 10
1520 ends in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 1520 within several notable number theory sequences:
Timeline
Deep dive
How 1520 breaks down
1520 carries 20 distinct factors and a digit signature of 8 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 2200, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10111110000 supports bitwise reasoning, hexadecimal 5F0 aligns with computing notation, and the Roman numeral MDXX keeps the encyclopedic tradition alive. These attributes make 1520 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1520 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1515–1525) to tune search ranges, and educators feature 1520 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 1520 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 1520
Is 1520 a prime number?
1520 is composite with 20 total factors and the prime factorization 2^4 × 5 × 19.
What is the prime factorization of 1520?
It breaks down as 2^4 × 5 × 19, multiplying the primes 2 × 2 × 2 × 2 × 5 × 19.
How is 1520 represented in binary and hexadecimal?
1520 converts to 10111110000 in binary and 5F0 in hexadecimal, which are helpful for computer science applications.
Is 1520 a perfect square, cube, or triangular number?
1520 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1520?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.