315
315 is a odd composite number that follows 314 and precedes 316. It is composed of 12 distinct factors: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Its prime factorization can be written as 3^2 × 5 × 7. 315 is classified as a deficient number based on the sum of its proper divisors. In computer science, 315 is represented as 100111011 in binary and 13B in hexadecimal. Historically, it is written as CCCXV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3^2 × 5 × 7) reveals 4 prime building blocks.
Divisible by 2
315 ends in 5, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 15 are not divisible by 4.
Divisible by 5
315 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 9 is a multiple of 9.
Divisible by 10
315 does not end in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Deficient classification and digit analytics place 315 within several notable number theory sequences:
Timeline
Deep dive
How 315 breaks down
315 carries 12 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 309, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100111011 supports bitwise reasoning, hexadecimal 13B aligns with computing notation, and the Roman numeral CCCXV keeps the encyclopedic tradition alive. These attributes make 315 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 315 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (310–320) to tune search ranges, and educators feature 315 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 315 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 315
Is 315 a prime number?
315 is composite with 12 total factors and the prime factorization 3^2 × 5 × 7.
What is the prime factorization of 315?
It breaks down as 3^2 × 5 × 7, multiplying the primes 3 × 3 × 5 × 7.
How is 315 represented in binary and hexadecimal?
315 converts to 100111011 in binary and 13B in hexadecimal, which are helpful for computer science applications.
Is 315 a perfect square, cube, or triangular number?
315 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 315?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.