7140
7140 is a even composite number that follows 7139 and precedes 7141. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140. Its prime factorization can be written as 2^2 × 3 × 5 × 7 × 17. 7140 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7140 is represented as 1101111100100 in binary and 1BE4 in hexadecimal. It also belongs to the triangular number sequence.
Factor Analysis
48 FactorsProperties
The prime factorization (2^2 × 3 × 5 × 7 × 17) reveals 6 prime building blocks.
Divisible by 2
7140 ends in 0, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
7140 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 12 is not a multiple of 9.
Divisible by 10
7140 ends in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Abundant classification and digit analytics place 7140 within several notable number theory sequences:
Timeline
Deep dive
How 7140 breaks down
7140 carries 48 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 17052, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101111100100 supports bitwise reasoning, hexadecimal 1BE4 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7140 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7140 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7135–7145) to tune search ranges, and educators feature 7140 in worksheets about factor trees. Its binary footprint of length 13 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 7140 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 7140
Is 7140 a prime number?
7140 is composite with 48 total factors and the prime factorization 2^2 × 3 × 5 × 7 × 17.
What is the prime factorization of 7140?
It breaks down as 2^2 × 3 × 5 × 7 × 17, multiplying the primes 2 × 2 × 3 × 5 × 7 × 17.
How is 7140 represented in binary and hexadecimal?
7140 converts to 1101111100100 in binary and 1BE4 in hexadecimal, which are helpful for computer science applications.
Is 7140 a perfect square, cube, or triangular number?
7140 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 7140?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.