1134
1134 is a even composite number that follows 1133 and precedes 1135. It is composed of 20 distinct factors: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 378, 567, 1134. Its prime factorization can be written as 2 × 3^4 × 7. 1134 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1134 is represented as 10001101110 in binary and 46E in hexadecimal. Historically, it is written as MCXXXIV in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2 × 3^4 × 7) reveals 6 prime building blocks.
Divisible by 2
1134 ends in 4, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 34 are not divisible by 4.
Divisible by 5
1134 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 9 is a multiple of 9.
Divisible by 10
1134 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 1134 within several notable number theory sequences:
Timeline
Deep dive
How 1134 breaks down
1134 carries 20 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1770, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10001101110 supports bitwise reasoning, hexadecimal 46E aligns with computing notation, and the Roman numeral MCXXXIV keeps the encyclopedic tradition alive. These attributes make 1134 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1134 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1129–1139) to tune search ranges, and educators feature 1134 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) help historians, numerologists, and trivia writers tie 1134 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 1134
Is 1134 a prime number?
1134 is composite with 20 total factors and the prime factorization 2 × 3^4 × 7.
What is the prime factorization of 1134?
It breaks down as 2 × 3^4 × 7, multiplying the primes 2 × 3 × 3 × 3 × 3 × 7.
How is 1134 represented in binary and hexadecimal?
1134 converts to 10001101110 in binary and 46E in hexadecimal, which are helpful for computer science applications.
Is 1134 a perfect square, cube, or triangular number?
1134 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1134?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.