213
213 is a odd composite number that follows 212 and precedes 214. It is composed of 4 distinct factors: 1, 3, 71, 213. Its prime factorization can be written as 3 × 71. 213 is classified as a deficient number based on the sum of its proper divisors. In computer science, 213 is represented as 11010101 in binary and D5 in hexadecimal. Historically, it is written as CCXIII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (3 × 71) reveals 2 prime building blocks.
Divisible by 2
213 ends in 3, so it is odd.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
213 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
213 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Deficient classification and digit analytics place 213 within several notable number theory sequences:
Timeline
Deep dive
How 213 breaks down
213 carries 4 distinct factors and a digit signature of 6 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 75, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010101 supports bitwise reasoning, hexadecimal D5 aligns with computing notation, and the Roman numeral CCXIII keeps the encyclopedic tradition alive. These attributes make 213 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 213 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (208–218) to tune search ranges, and educators feature 213 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) help historians, numerologists, and trivia writers tie 213 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 213
Is 213 a prime number?
213 is composite with 4 total factors and the prime factorization 3 × 71.
What is the prime factorization of 213?
It breaks down as 3 × 71, multiplying the primes 3 × 71.
How is 213 represented in binary and hexadecimal?
213 converts to 11010101 in binary and D5 in hexadecimal, which are helpful for computer science applications.
Is 213 a perfect square, cube, or triangular number?
213 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 213?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.