872
872 is a even composite number that follows 871 and precedes 873. It is composed of 8 distinct factors: 1, 2, 4, 8, 109, 218, 436, 872. Its prime factorization can be written as 2^3 × 109. 872 is classified as a deficient number based on the sum of its proper divisors. In computer science, 872 is represented as 1101101000 in binary and 368 in hexadecimal. Historically, it is written as DCCCLXXII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2^3 × 109) reveals 4 prime building blocks.
Divisible by 2
872 ends in 2, so it is even.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
872 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 17 is not a multiple of 9.
Divisible by 10
872 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 872 within several notable number theory sequences:
Timeline
Deep dive
How 872 breaks down
872 carries 8 distinct factors and a digit signature of 17 (8 as the digital root). The deficient classification indicates that its proper divisors sum to 778, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101101000 supports bitwise reasoning, hexadecimal 368 aligns with computing notation, and the Roman numeral DCCCLXXII keeps the encyclopedic tradition alive. These attributes make 872 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 872 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (867–877) to tune search ranges, and educators feature 872 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 872 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 872
Is 872 a prime number?
872 is composite with 8 total factors and the prime factorization 2^3 × 109.
What is the prime factorization of 872?
It breaks down as 2^3 × 109, multiplying the primes 2 × 2 × 2 × 109.
How is 872 represented in binary and hexadecimal?
872 converts to 1101101000 in binary and 368 in hexadecimal, which are helpful for computer science applications.
Is 872 a perfect square, cube, or triangular number?
872 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 872?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.