1215
1215 is a odd composite number that follows 1214 and precedes 1216. It is composed of 12 distinct factors: 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215. Its prime factorization can be written as 3^5 × 5. 1215 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1215 is represented as 10010111111 in binary and 4BF in hexadecimal. Historically, it is written as MCCXV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3^5 × 5) reveals 6 prime building blocks.
Divisible by 2
1215 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
1215 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
1215 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Deficient classification and digit analytics place 1215 within several notable number theory sequences:
Timeline
Deep dive
How 1215 breaks down
1215 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 969, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10010111111 supports bitwise reasoning, hexadecimal 4BF aligns with computing notation, and the Roman numeral MCCXV keeps the encyclopedic tradition alive. These attributes make 1215 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1215 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1210–1220) to tune search ranges, and educators feature 1215 in worksheets about factor trees. Its binary footprint of length 11 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 1215 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 1215
Is 1215 a prime number?
1215 is composite with 12 total factors and the prime factorization 3^5 × 5.
What is the prime factorization of 1215?
It breaks down as 3^5 × 5, multiplying the primes 3 × 3 × 3 × 3 × 3 × 5.
How is 1215 represented in binary and hexadecimal?
1215 converts to 10010111111 in binary and 4BF in hexadecimal, which are helpful for computer science applications.
Is 1215 a perfect square, cube, or triangular number?
1215 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1215?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.