343
343 is a odd composite number that follows 342 and precedes 344. It is composed of 4 distinct factors: 1, 7, 49, 343. Its prime factorization can be written as 7^3. 343 is classified as a deficient number based on the sum of its proper divisors. In computer science, 343 is represented as 101010111 in binary and 157 in hexadecimal. Historically, it is written as CCCXLIII in Roman numerals. It also belongs to the perfect cube sequence.
Factor Analysis
4 FactorsProperties
The prime factorization (7^3) reveals 3 prime building blocks.
Divisible by 2
343 ends in 3, so it is odd.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 43 are not divisible by 4.
Divisible by 5
343 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 10 is not a multiple of 9.
Divisible by 10
343 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Deficient classification and digit analytics place 343 within several notable number theory sequences:
Timeline
Deep dive
How 343 breaks down
343 carries 4 distinct factors and a digit signature of 10 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 57, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101010111 supports bitwise reasoning, hexadecimal 157 aligns with computing notation, and the Roman numeral CCCXLIII keeps the encyclopedic tradition alive. These attributes make 343 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 343 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (338–348) to tune search ranges, and educators feature 343 in worksheets about factor trees. Its binary footprint of length 9 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers, Perfect cubes) help historians, numerologists, and trivia writers tie 343 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 343
Is 343 a prime number?
343 is composite with 4 total factors and the prime factorization 7^3.
What is the prime factorization of 343?
It breaks down as 7^3, multiplying the primes 7 × 7 × 7.
How is 343 represented in binary and hexadecimal?
343 converts to 101010111 in binary and 157 in hexadecimal, which are helpful for computer science applications.
Is 343 a perfect square, cube, or triangular number?
343 is not a perfect square, is a perfect cube, and is not triangular.
What are the digit sum and digital root of 343?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.