345
345 is a odd composite number that follows 344 and precedes 346. It is composed of 8 distinct factors: 1, 3, 5, 15, 23, 69, 115, 345. Its prime factorization can be written as 3 × 5 × 23. 345 is classified as a deficient number based on the sum of its proper divisors. In computer science, 345 is represented as 101011001 in binary and 159 in hexadecimal. Historically, it is written as CCCXLV in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 5 × 23) reveals 3 prime building blocks.
Divisible by 2
345 ends in 5, so it is odd.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 45 are not divisible by 4.
Divisible by 5
345 ends in 5, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 12 is not a multiple of 9.
Divisible by 10
345 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 345 within several notable number theory sequences:
Timeline
Deep dive
How 345 breaks down
345 carries 8 distinct factors and a digit signature of 12 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 231, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101011001 supports bitwise reasoning, hexadecimal 159 aligns with computing notation, and the Roman numeral CCCXLV keeps the encyclopedic tradition alive. These attributes make 345 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 345 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (340–350) to tune search ranges, and educators feature 345 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 345 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 345
Is 345 a prime number?
345 is composite with 8 total factors and the prime factorization 3 × 5 × 23.
What is the prime factorization of 345?
It breaks down as 3 × 5 × 23, multiplying the primes 3 × 5 × 23.
How is 345 represented in binary and hexadecimal?
345 converts to 101011001 in binary and 159 in hexadecimal, which are helpful for computer science applications.
Is 345 a perfect square, cube, or triangular number?
345 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 345?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.