1296
1296 is a even composite number that follows 1295 and precedes 1297. It is composed of 25 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, 1296. Its prime factorization can be written as 2^4 × 3^4. 1296 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1296 is represented as 10100010000 in binary and 510 in hexadecimal. Historically, it is written as MCCXCVI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
25 FactorsProperties
The prime factorization (2^4 × 3^4) reveals 8 prime building blocks.
Divisible by 2
1296 ends in 6, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 96 form a multiple of 4.
Divisible by 5
1296 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 18 is a multiple of 9.
Divisible by 10
1296 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 1296 within several notable number theory sequences:
Timeline
Deep dive
How 1296 breaks down
1296 carries 25 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 2455, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10100010000 supports bitwise reasoning, hexadecimal 510 aligns with computing notation, and the Roman numeral MCCXCVI keeps the encyclopedic tradition alive. These attributes make 1296 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1296 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1291–1301) to tune search ranges, and educators feature 1296 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, Abundant numbers, Perfect squares) help historians, numerologists, and trivia writers tie 1296 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 1296
Is 1296 a prime number?
1296 is composite with 25 total factors and the prime factorization 2^4 × 3^4.
What is the prime factorization of 1296?
It breaks down as 2^4 × 3^4, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3.
How is 1296 represented in binary and hexadecimal?
1296 converts to 10100010000 in binary and 510 in hexadecimal, which are helpful for computer science applications.
Is 1296 a perfect square, cube, or triangular number?
1296 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1296?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.