340
340 is a even composite number that follows 339 and precedes 341. It is composed of 12 distinct factors: 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340. Its prime factorization can be written as 2^2 × 5 × 17. 340 is classified as a abundant number based on the sum of its proper divisors. In computer science, 340 is represented as 101010100 in binary and 154 in hexadecimal. Historically, it is written as CCCXL in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 5 × 17) reveals 4 prime building blocks.
Divisible by 2
340 ends in 0, so it is even.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
340 ends in 0, 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 7 is not a multiple of 9.
Divisible by 10
340 ends in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 340 within several notable number theory sequences:
Timeline
Deep dive
How 340 breaks down
340 carries 12 distinct factors and a digit signature of 7 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 416, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101010100 supports bitwise reasoning, hexadecimal 154 aligns with computing notation, and the Roman numeral CCCXL keeps the encyclopedic tradition alive. These attributes make 340 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 340 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (335–345) to tune search ranges, and educators feature 340 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, Abundant numbers) help historians, numerologists, and trivia writers tie 340 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 340
Is 340 a prime number?
340 is composite with 12 total factors and the prime factorization 2^2 × 5 × 17.
What is the prime factorization of 340?
It breaks down as 2^2 × 5 × 17, multiplying the primes 2 × 2 × 5 × 17.
How is 340 represented in binary and hexadecimal?
340 converts to 101010100 in binary and 154 in hexadecimal, which are helpful for computer science applications.
Is 340 a perfect square, cube, or triangular number?
340 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 340?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.