1331
1331 is a odd composite number that follows 1330 and precedes 1332. It is composed of 4 distinct factors: 1, 11, 121, 1331. Its prime factorization can be written as 11^3. 1331 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1331 is represented as 10100110011 in binary and 533 in hexadecimal. Historically, it is written as MCCCXXXI in Roman numerals. It also belongs to the perfect cube sequence.
Factor Analysis
4 FactorsProperties
The prime factorization (11^3) reveals 3 prime building blocks.
Divisible by 2
1331 ends in 1, so it is odd.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 31 are not divisible by 4.
Divisible by 5
1331 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 8 is not a multiple of 9.
Divisible by 10
1331 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 1331 within several notable number theory sequences:
Timeline
Deep dive
How 1331 breaks down
1331 carries 4 distinct factors and a digit signature of 8 (8 as the digital root). The deficient classification indicates that its proper divisors sum to 133, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10100110011 supports bitwise reasoning, hexadecimal 533 aligns with computing notation, and the Roman numeral MCCCXXXI keeps the encyclopedic tradition alive. These attributes make 1331 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1331 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1326–1336) to tune search ranges, and educators feature 1331 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, Perfect cubes) help historians, numerologists, and trivia writers tie 1331 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 1331
Is 1331 a prime number?
1331 is composite with 4 total factors and the prime factorization 11^3.
What is the prime factorization of 1331?
It breaks down as 11^3, multiplying the primes 11 × 11 × 11.
How is 1331 represented in binary and hexadecimal?
1331 converts to 10100110011 in binary and 533 in hexadecimal, which are helpful for computer science applications.
Is 1331 a perfect square, cube, or triangular number?
1331 is not a perfect square, is a perfect cube, and is not triangular.
What are the digit sum and digital root of 1331?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.