231
231 is a odd composite number that follows 230 and precedes 232. It is composed of 8 distinct factors: 1, 3, 7, 11, 21, 33, 77, 231. Its prime factorization can be written as 3 × 7 × 11. 231 is classified as a deficient number based on the sum of its proper divisors. In computer science, 231 is represented as 11100111 in binary and E7 in hexadecimal. Historically, it is written as CCXXXI in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 7 × 11) reveals 3 prime building blocks.
Divisible by 2
231 ends in 1, so it is odd.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 31 are not divisible by 4.
Divisible by 5
231 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 6 is not a multiple of 9.
Divisible by 10
231 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 231 within several notable number theory sequences:
Timeline
Deep dive
How 231 breaks down
231 carries 8 distinct factors and a digit signature of 6 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 153, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100111 supports bitwise reasoning, hexadecimal E7 aligns with computing notation, and the Roman numeral CCXXXI keeps the encyclopedic tradition alive. These attributes make 231 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 231 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (226–236) to tune search ranges, and educators feature 231 in worksheets about factor trees. Its binary footprint of length 8 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 231 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 231
Is 231 a prime number?
231 is composite with 8 total factors and the prime factorization 3 × 7 × 11.
What is the prime factorization of 231?
It breaks down as 3 × 7 × 11, multiplying the primes 3 × 7 × 11.
How is 231 represented in binary and hexadecimal?
231 converts to 11100111 in binary and E7 in hexadecimal, which are helpful for computer science applications.
Is 231 a perfect square, cube, or triangular number?
231 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 231?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.