521
521 is a odd prime number that follows 520 and precedes 522. As a prime number, 521 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 521. 521 is classified as a deficient number based on the sum of its proper divisors. In computer science, 521 is represented as 1000001001 in binary and 209 in hexadecimal. Historically, it is written as DXXI in Roman numerals.
Factor Analysis
2 FactorsProperties
521 is prime, so its only factors are 1 and 521.
Divisible by 2
521 ends in 1, so it is odd.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 21 are not divisible by 4.
Divisible by 5
521 does not end in 0 or 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
521 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Deficient classification and digit analytics place 521 within several notable number theory sequences:
Timeline
Deep dive
How 521 breaks down
521 carries 2 distinct factors and a digit signature of 8 (8 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000001001 supports bitwise reasoning, hexadecimal 209 aligns with computing notation, and the Roman numeral DXXI keeps the encyclopedic tradition alive. These attributes make 521 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 521 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (516–526) to tune search ranges, and educators feature 521 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 521 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 521
Is 521 a prime number?
521 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 521?
521 is already prime, so the factorization is simply 521.
How is 521 represented in binary and hexadecimal?
521 converts to 1000001001 in binary and 209 in hexadecimal, which are helpful for computer science applications.
Is 521 a perfect square, cube, or triangular number?
521 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 521?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.