561
561 is a odd composite number that follows 560 and precedes 562. It is composed of 8 distinct factors: 1, 3, 11, 17, 33, 51, 187, 561. Its prime factorization can be written as 3 × 11 × 17. 561 is classified as a deficient number based on the sum of its proper divisors. In computer science, 561 is represented as 1000110001 in binary and 231 in hexadecimal. Historically, it is written as DLXI in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 11 × 17) reveals 3 prime building blocks.
Divisible by 2
561 ends in 1, so it is odd.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 61 are not divisible by 4.
Divisible by 5
561 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 12 is not a multiple of 9.
Divisible by 10
561 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 561 within several notable number theory sequences:
Timeline
Deep dive
How 561 breaks down
561 carries 8 distinct factors and a digit signature of 12 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 303, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1000110001 supports bitwise reasoning, hexadecimal 231 aligns with computing notation, and the Roman numeral DLXI keeps the encyclopedic tradition alive. These attributes make 561 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 561 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (556–566) to tune search ranges, and educators feature 561 in worksheets about factor trees. 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 (Composite numbers, Deficient numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 561 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 561
Is 561 a prime number?
561 is composite with 8 total factors and the prime factorization 3 × 11 × 17.
What is the prime factorization of 561?
It breaks down as 3 × 11 × 17, multiplying the primes 3 × 11 × 17.
How is 561 represented in binary and hexadecimal?
561 converts to 1000110001 in binary and 231 in hexadecimal, which are helpful for computer science applications.
Is 561 a perfect square, cube, or triangular number?
561 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 561?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.