7998
7998 is a even composite number that follows 7997 and precedes 7999. It is composed of 16 distinct factors: 1, 2, 3, 6, 31, 43, 62, 86, 93, 129, 186, 258, 1333, 2666, 3999, 7998. Its prime factorization can be written as 2 × 3 × 31 × 43. 7998 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7998 is represented as 1111100111110 in binary and 1F3E in hexadecimal.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3 × 31 × 43) reveals 4 prime building blocks.
Divisible by 2
7998 ends in 8, so it is even.
Divisible by 3
The digit sum 33 is a multiple of 3.
Divisible by 4
The last two digits 98 are not divisible by 4.
Divisible by 5
7998 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 33 is not a multiple of 9.
Divisible by 10
7998 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 7998 within several notable number theory sequences:
Timeline
Deep dive
How 7998 breaks down
7998 carries 16 distinct factors and a digit signature of 33 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 8898, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111100111110 supports bitwise reasoning, hexadecimal 1F3E aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7998 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7998 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7993–8003) to tune search ranges, and educators feature 7998 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 7998 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 7998
Is 7998 a prime number?
7998 is composite with 16 total factors and the prime factorization 2 × 3 × 31 × 43.
What is the prime factorization of 7998?
It breaks down as 2 × 3 × 31 × 43, multiplying the primes 2 × 3 × 31 × 43.
How is 7998 represented in binary and hexadecimal?
7998 converts to 1111100111110 in binary and 1F3E in hexadecimal, which are helpful for computer science applications.
Is 7998 a perfect square, cube, or triangular number?
7998 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7998?
The digits sum to 33, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.