3213
3213 is a odd composite number that follows 3212 and precedes 3214. It is composed of 16 distinct factors: 1, 3, 7, 9, 17, 21, 27, 51, 63, 119, 153, 189, 357, 459, 1071, 3213. Its prime factorization can be written as 3^3 × 7 × 17. 3213 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3213 is represented as 110010001101 in binary and C8D in hexadecimal. Historically, it is written as MMMCCXIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (3^3 × 7 × 17) reveals 5 prime building blocks.
Divisible by 2
3213 ends in 3, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
3213 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 9 is a multiple of 9.
Divisible by 10
3213 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Deficient classification and digit analytics place 3213 within several notable number theory sequences:
Timeline
Deep dive
How 3213 breaks down
3213 carries 16 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 2547, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010001101 supports bitwise reasoning, hexadecimal C8D aligns with computing notation, and the Roman numeral MMMCCXIII keeps the encyclopedic tradition alive. These attributes make 3213 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3213 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3208–3218) to tune search ranges, and educators feature 3213 in worksheets about factor trees. Its binary footprint of length 12 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 3213 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 3213
Is 3213 a prime number?
3213 is composite with 16 total factors and the prime factorization 3^3 × 7 × 17.
What is the prime factorization of 3213?
It breaks down as 3^3 × 7 × 17, multiplying the primes 3 × 3 × 3 × 7 × 17.
How is 3213 represented in binary and hexadecimal?
3213 converts to 110010001101 in binary and C8D in hexadecimal, which are helpful for computer science applications.
Is 3213 a perfect square, cube, or triangular number?
3213 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3213?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.