852
852 is a even composite number that follows 851 and precedes 853. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852. Its prime factorization can be written as 2^2 × 3 × 71. 852 is classified as a abundant number based on the sum of its proper divisors. In computer science, 852 is represented as 1101010100 in binary and 354 in hexadecimal. Historically, it is written as DCCCLII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3 × 71) reveals 4 prime building blocks.
Divisible by 2
852 ends in 2, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 52 form a multiple of 4.
Divisible by 5
852 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 15 is not a multiple of 9.
Divisible by 10
852 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 852 within several notable number theory sequences:
Timeline
Deep dive
How 852 breaks down
852 carries 12 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 1164, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101010100 supports bitwise reasoning, hexadecimal 354 aligns with computing notation, and the Roman numeral DCCCLII keeps the encyclopedic tradition alive. These attributes make 852 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 852 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (847–857) to tune search ranges, and educators feature 852 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, Abundant numbers) help historians, numerologists, and trivia writers tie 852 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 852
Is 852 a prime number?
852 is composite with 12 total factors and the prime factorization 2^2 × 3 × 71.
What is the prime factorization of 852?
It breaks down as 2^2 × 3 × 71, multiplying the primes 2 × 2 × 3 × 71.
How is 852 represented in binary and hexadecimal?
852 converts to 1101010100 in binary and 354 in hexadecimal, which are helpful for computer science applications.
Is 852 a perfect square, cube, or triangular number?
852 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 852?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.