1521
1521 is a odd composite number that follows 1520 and precedes 1522. It is composed of 9 distinct factors: 1, 3, 9, 13, 39, 117, 169, 507, 1521. Its prime factorization can be written as 3^2 × 13^2. 1521 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1521 is represented as 10111110001 in binary and 5F1 in hexadecimal. Historically, it is written as MDXXI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
9 FactorsProperties
The prime factorization (3^2 × 13^2) reveals 4 prime building blocks.
Divisible by 2
1521 ends in 1, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 21 are not divisible by 4.
Divisible by 5
1521 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 9 is a multiple of 9.
Divisible by 10
1521 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Deficient classification and digit analytics place 1521 within several notable number theory sequences:
Timeline
Deep dive
How 1521 breaks down
1521 carries 9 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 858, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10111110001 supports bitwise reasoning, hexadecimal 5F1 aligns with computing notation, and the Roman numeral MDXXI keeps the encyclopedic tradition alive. These attributes make 1521 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1521 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1516–1526) to tune search ranges, and educators feature 1521 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, Deficient numbers, Perfect squares) help historians, numerologists, and trivia writers tie 1521 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 1521
Is 1521 a prime number?
1521 is composite with 9 total factors and the prime factorization 3^2 × 13^2.
What is the prime factorization of 1521?
It breaks down as 3^2 × 13^2, multiplying the primes 3 × 3 × 13 × 13.
How is 1521 represented in binary and hexadecimal?
1521 converts to 10111110001 in binary and 5F1 in hexadecimal, which are helpful for computer science applications.
Is 1521 a perfect square, cube, or triangular number?
1521 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1521?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.