338
338 is a even composite number that follows 337 and precedes 339. It is composed of 6 distinct factors: 1, 2, 13, 26, 169, 338. Its prime factorization can be written as 2 × 13^2. 338 is classified as a deficient number based on the sum of its proper divisors. In computer science, 338 is represented as 101010010 in binary and 152 in hexadecimal. Historically, it is written as CCCXXXVIII in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (2 × 13^2) reveals 3 prime building blocks.
Divisible by 2
338 ends in 8, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 38 are not divisible by 4.
Divisible by 5
338 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 14 is not a multiple of 9.
Divisible by 10
338 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Deficient classification and digit analytics place 338 within several notable number theory sequences:
Timeline
Deep dive
How 338 breaks down
338 carries 6 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 211, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101010010 supports bitwise reasoning, hexadecimal 152 aligns with computing notation, and the Roman numeral CCCXXXVIII keeps the encyclopedic tradition alive. These attributes make 338 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 338 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (333–343) to tune search ranges, and educators feature 338 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) help historians, numerologists, and trivia writers tie 338 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 338
Is 338 a prime number?
338 is composite with 6 total factors and the prime factorization 2 × 13^2.
What is the prime factorization of 338?
It breaks down as 2 × 13^2, multiplying the primes 2 × 13 × 13.
How is 338 represented in binary and hexadecimal?
338 converts to 101010010 in binary and 152 in hexadecimal, which are helpful for computer science applications.
Is 338 a perfect square, cube, or triangular number?
338 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 338?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.