27440
27440 is a even composite number that follows 27439 and precedes 27441. It is composed of 40 distinct factors: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 49, 56, 70, 80, 98, 112, 140, 196, 245, 280, 343, 392, 490, 560, 686, 784, 980, 1372, 1715, 1960, 2744, 3430, 3920, 5488, 6860, 13720, 27440. Its prime factorization can be written as 2^4 × 5 × 7^3. 27440 is classified as a abundant number based on the sum of its proper divisors. In computer science, 27440 is represented as 110101100110000 in binary and 6B30 in hexadecimal.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 5 × 7^3) reveals 8 prime building blocks.
Divisible by 2
27440 ends in 0, so it is even.
Divisible by 3
The digit sum 17 is not a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
27440 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 17 is not a multiple of 9.
Divisible by 10
27440 ends in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Abundant classification and digit analytics place 27440 within several notable number theory sequences:
Timeline
Deep dive
How 27440 breaks down
27440 carries 40 distinct factors and a digit signature of 17 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 46960, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110101100110000 supports bitwise reasoning, hexadecimal 6B30 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 27440 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 27440 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (27435–27445) to tune search ranges, and educators feature 27440 in worksheets about factor trees. Its binary footprint of length 15 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 27440 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 27440
Is 27440 a prime number?
27440 is composite with 40 total factors and the prime factorization 2^4 × 5 × 7^3.
What is the prime factorization of 27440?
It breaks down as 2^4 × 5 × 7^3, multiplying the primes 2 × 2 × 2 × 2 × 5 × 7 × 7 × 7.
How is 27440 represented in binary and hexadecimal?
27440 converts to 110101100110000 in binary and 6B30 in hexadecimal, which are helpful for computer science applications.
Is 27440 a perfect square, cube, or triangular number?
27440 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 27440?
The digits sum to 17, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.