825
825 is a odd composite number that follows 824 and precedes 826. It is composed of 12 distinct factors: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825. Its prime factorization can be written as 3 × 5^2 × 11. 825 is classified as a deficient number based on the sum of its proper divisors. In computer science, 825 is represented as 1100111001 in binary and 339 in hexadecimal. Historically, it is written as DCCCXXV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3 × 5^2 × 11) reveals 4 prime building blocks.
Divisible by 2
825 ends in 5, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 25 are not divisible by 4.
Divisible by 5
825 ends in 5, 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 15 is not a multiple of 9.
Divisible by 10
825 does not end in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Deficient classification and digit analytics place 825 within several notable number theory sequences:
Timeline
Deep dive
How 825 breaks down
825 carries 12 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 663, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100111001 supports bitwise reasoning, hexadecimal 339 aligns with computing notation, and the Roman numeral DCCCXXV keeps the encyclopedic tradition alive. These attributes make 825 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 825 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (820–830) to tune search ranges, and educators feature 825 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) help historians, numerologists, and trivia writers tie 825 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 825
Is 825 a prime number?
825 is composite with 12 total factors and the prime factorization 3 × 5^2 × 11.
What is the prime factorization of 825?
It breaks down as 3 × 5^2 × 11, multiplying the primes 3 × 5 × 5 × 11.
How is 825 represented in binary and hexadecimal?
825 converts to 1100111001 in binary and 339 in hexadecimal, which are helpful for computer science applications.
Is 825 a perfect square, cube, or triangular number?
825 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 825?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.