31648
31648 is a even composite number that follows 31647 and precedes 31649. It is composed of 24 distinct factors: 1, 2, 4, 8, 16, 23, 32, 43, 46, 86, 92, 172, 184, 344, 368, 688, 736, 989, 1376, 1978, 3956, 7912, 15824, 31648. Its prime factorization can be written as 2^5 × 23 × 43. 31648 is classified as a abundant number based on the sum of its proper divisors. In computer science, 31648 is represented as 111101110100000 in binary and 7BA0 in hexadecimal.
Factor Analysis
24 FactorsProperties
The prime factorization (2^5 × 23 × 43) reveals 7 prime building blocks.
Divisible by 2
31648 ends in 8, so it is even.
Divisible by 3
The digit sum 22 is not a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
31648 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 22 is not a multiple of 9.
Divisible by 10
31648 does not end in 0.
Divisible by 11
The alternating digit sum 12 is not a multiple of 11.
Abundant classification and digit analytics place 31648 within several notable number theory sequences:
Timeline
Deep dive
How 31648 breaks down
31648 carries 24 distinct factors and a digit signature of 22 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 34880, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111101110100000 supports bitwise reasoning, hexadecimal 7BA0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 31648 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 31648 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (31643–31653) to tune search ranges, and educators feature 31648 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 31648 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 31648
Is 31648 a prime number?
31648 is composite with 24 total factors and the prime factorization 2^5 × 23 × 43.
What is the prime factorization of 31648?
It breaks down as 2^5 × 23 × 43, multiplying the primes 2 × 2 × 2 × 2 × 2 × 23 × 43.
How is 31648 represented in binary and hexadecimal?
31648 converts to 111101110100000 in binary and 7BA0 in hexadecimal, which are helpful for computer science applications.
Is 31648 a perfect square, cube, or triangular number?
31648 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 31648?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.