7938
7938 is a even composite number that follows 7937 and precedes 7939. It is composed of 30 distinct factors: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 49, 54, 63, 81, 98, 126, 147, 162, 189, 294, 378, 441, 567, 882, 1134, 1323, 2646, 3969, 7938. Its prime factorization can be written as 2 × 3^4 × 7^2. 7938 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7938 is represented as 1111100000010 in binary and 1F02 in hexadecimal.
Factor Analysis
30 FactorsProperties
The prime factorization (2 × 3^4 × 7^2) reveals 7 prime building blocks.
Divisible by 2
7938 ends in 8, so it is even.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 38 are not divisible by 4.
Divisible by 5
7938 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 27 is a multiple of 9.
Divisible by 10
7938 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Abundant classification and digit analytics place 7938 within several notable number theory sequences:
Timeline
Deep dive
How 7938 breaks down
7938 carries 30 distinct factors and a digit signature of 27 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 12753, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111100000010 supports bitwise reasoning, hexadecimal 1F02 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7938 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7938 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7933–7943) to tune search ranges, and educators feature 7938 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) help historians, numerologists, and trivia writers tie 7938 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 7938
Is 7938 a prime number?
7938 is composite with 30 total factors and the prime factorization 2 × 3^4 × 7^2.
What is the prime factorization of 7938?
It breaks down as 2 × 3^4 × 7^2, multiplying the primes 2 × 3 × 3 × 3 × 3 × 7 × 7.
How is 7938 represented in binary and hexadecimal?
7938 converts to 1111100000010 in binary and 1F02 in hexadecimal, which are helpful for computer science applications.
Is 7938 a perfect square, cube, or triangular number?
7938 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7938?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.