8000
8000 is a even composite number that follows 7999 and precedes 8001. It is composed of 28 distinct factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 800, 1000, 1600, 2000, 4000, 8000. Its prime factorization can be written as 2^6 × 5^3. 8000 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8000 is represented as 1111101000000 in binary and 1F40 in hexadecimal. It also belongs to the perfect cube sequence.
Factor Analysis
28 FactorsProperties
The prime factorization (2^6 × 5^3) reveals 9 prime building blocks.
Divisible by 2
8000 ends in 0, so it is even.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
8000 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 8 is not a multiple of 9.
Divisible by 10
8000 ends in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 8000 within several notable number theory sequences:
Timeline
Deep dive
How 8000 breaks down
8000 carries 28 distinct factors and a digit signature of 8 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 11812, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111101000000 supports bitwise reasoning, hexadecimal 1F40 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8000 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8000 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7995–8005) to tune search ranges, and educators feature 8000 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, Perfect cubes) help historians, numerologists, and trivia writers tie 8000 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 8000
Is 8000 a prime number?
8000 is composite with 28 total factors and the prime factorization 2^6 × 5^3.
What is the prime factorization of 8000?
It breaks down as 2^6 × 5^3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5.
How is 8000 represented in binary and hexadecimal?
8000 converts to 1111101000000 in binary and 1F40 in hexadecimal, which are helpful for computer science applications.
Is 8000 a perfect square, cube, or triangular number?
8000 is not a perfect square, is a perfect cube, and is not triangular.
What are the digit sum and digital root of 8000?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.