693
693 is a odd composite number that follows 692 and precedes 694. It is composed of 12 distinct factors: 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693. Its prime factorization can be written as 3^2 × 7 × 11. 693 is classified as a deficient number based on the sum of its proper divisors. In computer science, 693 is represented as 1010110101 in binary and 2B5 in hexadecimal. Historically, it is written as DCXCIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3^2 × 7 × 11) reveals 4 prime building blocks.
Divisible by 2
693 ends in 3, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 93 are not divisible by 4.
Divisible by 5
693 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 18 is a multiple of 9.
Divisible by 10
693 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 693 within several notable number theory sequences:
Timeline
Deep dive
How 693 breaks down
693 carries 12 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 555, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010110101 supports bitwise reasoning, hexadecimal 2B5 aligns with computing notation, and the Roman numeral DCXCIII keeps the encyclopedic tradition alive. These attributes make 693 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 693 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (688–698) to tune search ranges, and educators feature 693 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 693 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 693
Is 693 a prime number?
693 is composite with 12 total factors and the prime factorization 3^2 × 7 × 11.
What is the prime factorization of 693?
It breaks down as 3^2 × 7 × 11, multiplying the primes 3 × 3 × 7 × 11.
How is 693 represented in binary and hexadecimal?
693 converts to 1010110101 in binary and 2B5 in hexadecimal, which are helpful for computer science applications.
Is 693 a perfect square, cube, or triangular number?
693 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 693?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.