8100
8100 is a even composite number that follows 8099 and precedes 8101. It is composed of 45 distinct factors: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 81, 90, 100, 108, 135, 150, 162, 180, 225, 270, 300, 324, 405, 450, 540, 675, 810, 900, 1350, 1620, 2025, 2700, 4050, 8100. Its prime factorization can be written as 2^2 × 3^4 × 5^2. 8100 is classified as a abundant number based on the sum of its proper divisors. In computer science, 8100 is represented as 1111110100100 in binary and 1FA4 in hexadecimal. It also belongs to the perfect square sequence.
Factor Analysis
45 FactorsProperties
The prime factorization (2^2 × 3^4 × 5^2) reveals 8 prime building blocks.
Divisible by 2
8100 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
8100 ends in 0, so it is divisible by 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 9 is a multiple of 9.
Divisible by 10
8100 ends in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 8100 within several notable number theory sequences:
Timeline
Deep dive
How 8100 breaks down
8100 carries 45 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 18157, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111110100100 supports bitwise reasoning, hexadecimal 1FA4 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 8100 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 8100 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (8095–8105) to tune search ranges, and educators feature 8100 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 squares) help historians, numerologists, and trivia writers tie 8100 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 8100
Is 8100 a prime number?
8100 is composite with 45 total factors and the prime factorization 2^2 × 3^4 × 5^2.
What is the prime factorization of 8100?
It breaks down as 2^2 × 3^4 × 5^2, multiplying the primes 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5.
How is 8100 represented in binary and hexadecimal?
8100 converts to 1111110100100 in binary and 1FA4 in hexadecimal, which are helpful for computer science applications.
Is 8100 a perfect square, cube, or triangular number?
8100 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 8100?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.