Find n-th Champernowne Digit. Calculate the n-th digit of Champernowne constant. Decode a Look-and-say Sequence. Perform the inverse operation on a look-and-say sequence. Generate P-adic Expansions. Calculate p-adic expansions of arbitrary numbers. Generate Pandigital Number Sequence. Create a list of pandigital numbers. Generate Stanley Number Sequence. Create a list of Stanley numbers. Generate Bell Number Sequence. Create a list of Bell numbers.
Generate Carmichael Number Sequence. Create a list of Charmichel numbers. Generate Catalan Number Sequence. Create a list of Catalan numbers. Generate Composite Number Sequence. Create a list of composite numbers. Generate Secant Number Sequence. Create a list of secant numbers. Generate Golomb Number Sequence. Create a list of Golomb-Silverman numbers. Generate Euler's Totient Number Sequence. Create a list of Euler's phi numbers.
Generate Juggler Number Sequence. Create a list of juggler numbers. Generate Lucky Number Sequence. Create a list of lucky numbers.
Generate Motzkin Number Sequence. Create a list of motzkin numbers. Generate Padovan Number Sequence. Create a list of Padovan numbers. Generate Pseudoperfect Number Sequence. Create a list of semiperfect numbers. Generate Ulam Number Sequence. Create a list of Ulam numbers. Generate Weird Number Sequence.
Create a list of weird numbers. Generate Superperfect Number Sequence. Create a list of superperfect numbers. Partition a Number. Find all partitions of the given integer. Generate Partition Number Sequence. Create a list of Partition function numbers. Generate Arithmetic Progression. Create an arithmetic sequence of numbers. Generate Geometric Progression.
Create a geometric sequence of numbers. Generate Polynomial Progression. Create a polynomial sequence of numbers. Generate Natural Number Sequence. Create a list of natural numbers. Generate Powers of Two. Create a list of numbers of powers of two. Generate Powers of Ten. Create a list of numbers of powers of ten. Generate a Sparse Matrix.
Generate a matrix with very few non-zero elements. Multiply a Matrix by a Scalar. Multiply all matrix elements by a number. Check if a Matrix is Singular. Determine if a matrix is degenerate. Find the Co-factor Matrix. Given a matrix, find its cofactor matrix. Find the Adjugate Matrix. Given a matrix, find its adjunct. LU Factor a Matrix. Decompose a matrix into LU factors.
Find Matrix Eigenvalues. Find eigenvalues of a matrix. Prettify a Matrix. Beautify a matrix by neatly aligning all its columns. Reformat a Matrix. Convert matrix in one format to another format. Draw a Fibonacci Spiral. Generate a Fibonacci spiral curve.
Draw a Theodorus Spiral. Generate a square root spiral. Draw a Fermat Spiral. Generate a parabolic spiral curve. Draw Fibonacci Rectangles. Generate a drawing of Fibonacci rectangles. Draw a Fibonacci Seed Head. Generate a Fibonacci flower head. Draw a Padovan Fractal. Generate a Padovan equiliteral triangles fractal. Draw a Apollonian Gasket. Generate an Apollonian gasket fractal. Draw a Mandelbrot Fractal. Generate a Mandelbrot fractal. Draw a Julia Fractal. Draw a Rauzy Fractal.
Draw Blancmange Fractal Curve. Generate a Blancmange fractal. The limit on the input number to factor is less than 10,,,, less than 10 trillion or a maximum of 13 digits. Prime factorization or integer factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number. This is also known as prime decomposition.
We cover two methods of prime factorization: find primes by trial division, and use primes to create a prime factors tree. Say you want to find the prime factors of using trial division.
We have taken the first step! But 6 is not a prime number, so we need to go further. Example: What is the prime factorization of ? Can we divide exactly by 2? The next prime, 5, does not work. This is essentially the "brute force" method for determining the prime factors of a number, and though is a simple example, it can get far more tedious very quickly. Another common way to conduct prime factorization is referred to as prime decomposition, and can involve the use of a factor tree.
Creating a factor tree involves breaking up the composite number into factors of the composite number, until all of the numbers are prime. In the example below, the prime factors are found by dividing by a prime factor, 2, then continuing to divide the result until all factors are prime.
The example below demonstrates two ways that a factor tree can be created using the number
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