6400
6400 is a even composite number that follows 6399 and precedes 6401. It is composed of 27 distinct factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 640, 800, 1280, 1600, 3200, 6400. Its prime factorization can be written as 2^8 × 5^2. 6400 is classified as a abundant number based on the sum of its proper divisors. In computer science, 6400 is represented as 1100100000000 in binary and 1900 in hexadecimal. It also belongs to the perfect square sequence.
Factor Analysis
27 FactorsProperties
The prime factorization (2^8 × 5^2) reveals 10 prime building blocks.
Divisible by 2
6400 ends in 0, so it is even.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
6400 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 10 is not a multiple of 9.
Divisible by 10
6400 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 6400 within several notable number theory sequences:
Timeline
Deep dive
How 6400 breaks down
6400 carries 27 distinct factors and a digit signature of 10 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 9441, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1100100000000 supports bitwise reasoning, hexadecimal 1900 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 6400 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 6400 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (6395–6405) to tune search ranges, and educators feature 6400 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 6400 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 6400
Is 6400 a prime number?
6400 is composite with 27 total factors and the prime factorization 2^8 × 5^2.
What is the prime factorization of 6400?
It breaks down as 2^8 × 5^2, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5.
How is 6400 represented in binary and hexadecimal?
6400 converts to 1100100000000 in binary and 1900 in hexadecimal, which are helpful for computer science applications.
Is 6400 a perfect square, cube, or triangular number?
6400 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 6400?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.