1140
1140 is a even composite number that follows 1139 and precedes 1141. It is composed of 24 distinct factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, 1140. Its prime factorization can be written as 2^2 × 3 × 5 × 19. 1140 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1140 is represented as 10001110100 in binary and 474 in hexadecimal. Historically, it is written as MCXL in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 5 × 19) reveals 5 prime building blocks.
Divisible by 2
1140 ends in 0, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
1140 ends in 0, so it is divisible by 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 6 is not a multiple of 9.
Divisible by 10
1140 ends in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 1140 within several notable number theory sequences:
Timeline
Deep dive
How 1140 breaks down
1140 carries 24 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2220, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10001110100 supports bitwise reasoning, hexadecimal 474 aligns with computing notation, and the Roman numeral MCXL keeps the encyclopedic tradition alive. These attributes make 1140 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1140 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1135–1145) to tune search ranges, and educators feature 1140 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 1140 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 1140
Is 1140 a prime number?
1140 is composite with 24 total factors and the prime factorization 2^2 × 3 × 5 × 19.
What is the prime factorization of 1140?
It breaks down as 2^2 × 3 × 5 × 19, multiplying the primes 2 × 2 × 3 × 5 × 19.
How is 1140 represented in binary and hexadecimal?
1140 converts to 10001110100 in binary and 474 in hexadecimal, which are helpful for computer science applications.
Is 1140 a perfect square, cube, or triangular number?
1140 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1140?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.